A. Davydov - Publications

2023

Davydov A., Marcugini S., Pambianco F., New bounds for covering codes of radius 3 and codimension 3t+1. Advances in Mathematics of Communications. 14 pages, doi: 10.3934/amc.2023042 http://iitp.ru/https://www.aimsciences.org/article/doi/10.3934/amc.2023042

Davydov A., Marcugini S., Pambianco F., Incidence matrices for the class O_6 of lines external to the twisted cubic in PG(3,q), Journal of Geometry, 2023, vol. 114, no. 2, article number 21, https://doi.org/10.1007/s00022-023-00678-2 http://iitp.ru/https://doi.org/10.1007/s00022-023-00678-2

Davydov A., Marcugini S., Pambianco F., Orbits of the class O_6 of lines external to the twisted cubic in PG(3, q), Mediterranean Journal of Mathematics, vol. 20, No. 3, article number 160 (2023) , https://doi.org/10.1007/s00009-023-02349-7 http://iitp.ru/https://doi.org/10.1007/s00009-023-02349-7

Davydov A., Marcugini S., Pambianco F., Orbits of lines for a twisted cubic in PG(3,q). Mediterranean Journal of Mathematics. vol. 20, No. 3, article number 132 (2023), https://doi.org/10.1007/s00009-023-02279-4 http://iitp.ru/https://doi.org/10.1007/s00009-023-02279-4

Davydov A., Marcugini S., Pambianco F., Upper bounds on the length function for covering codes with covering radius R and codimension tR+1, Advances in Mathematics of Communications, vol. 17, No. 1, February 2023, pp. 98-18, doi: 10.3934/amc.2021074 http://iitp.ru/https://www.aimsciences.org//article/doi/10.3934/amc.2021074

Davydov A., Marcugini S., Pambianco F., On the weight distribution of the cosets of MDS codes, Advances in Mathematics of Communications, Vol. 17, No. 5, October 2023, pp. 1115-1138, doi: 10.3934/amc.2021042 http://iitp.ru/https://www.aimsciences.org/article/doi/10.3934/amc.2021042

2022

Davydov A., Marcugini S., Pambianco F., Orbits of the class O_6 of lines external with respect to the twisted cubic in PG(3,q), electronic preprint, arXiv:2209.04910 [math.CO], [math.AG], 27 pages, 23 references. September 2022 http://iitp.ru/https://arxiv.org/abs/2209.04910

Davydov A., Marcugini S., Pambianco F., Incidence matrices for the class O_6 of lines external to the twisted cubic in PG(3,q), electronic preprint, arXiv:2210.12821 [math.CO], 27 pages, 32 references, 11 tables. October 2022 http://iitp.ru/https://arxiv.org/abs/2210.12821

Davydov A., Marcugini S., Pambianco F., Twisted cubic and plane-line incidence matrix in PG(3,q), Journal of Geometry, 2022, vol. 113, no. 2, article 29, https://doi.org/10.1007/s00022-022-00644-4, 29 pages http://iitp.ru/https://doi.org/10.1007/s00022-022-00644-4

2021

Davydov A., Marcugini S., Pambianco F., Upper bounds on the length function for covering codes with covering radius R and codimension tR+1, electronic preprint, arXiv:2108.13609v2 [cs.IT], 31 pages, 55 references, 1 table, 1 fig., November 2021 http://iitp.ru/https://arxiv.org/abs/2108.13609

Davydov A., Marcugini S., Pambianco F., On Cosets Weight Distribution of Doubly-Extended Reed-Solomon Codes of Codimension 4, IEEE Transactions on Information Theory, vol.: 67 (8), Aug. 2021, pp. 5088 - 5096 http://iitp.ru/https://ieeexplore.ieee.org/document/9454475

Davydov A., Marcugini S., Pambianco F., Twisted cubic and point-line incidence matrix in PG(3,q), Designs, Codes and Cryptography (2021), 23 pages http://iitp.ru/https://link.springer.com/article/10.1007/s10623-021-00911-6

Davydov A., Marcugini S., Pambianco F., Twisted cubic and point-line incidence matrix in PG(3,q), electronic preprint, arXiv:2104.12254v2 [math.CO], 30 pages, 28 references, 5 tables, July 2021 http://arxiv.org/abs/2104.12254

Davydov A., Marcugini S., Pambianco F., Twisted cubic and plane-line incidence matrix in PG(3,q), electronic preprint, arXiv:2103.11248v3 [math.CO], 29 pages, 2 tables, 24 references, Mar. 2021 http://iitp.ru/https://arxiv.org/abs/2103.11248

Davydov A., Marcugini S., Pambianco F., Twisted cubic and orbits of lines in PG(3,q), electronic preprint, arXiv:2103.12655v2 [math.CO], 27 pages, 19 references, Mar. 2021 http://iitp.ru/https://arxiv.org/abs/2103.12655

Davydov A., Marcugini S., Pambianco F., On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4, electronic preprint, arXiv:2007.08798v2 [cs.IT], 20 pages, 2 tables, 37 references, Feb. 2021 http://iitp.ru/https://arxiv.org/abs/2007.08798

Davydov A., Marcugini S., Pambianco F., On the weight distribution of the cosets of MDS codes, electronic preprint, arXiv:2101.12722 [cs.IT], 32 pages, 45 references, June. 2021 http://iitp.ru/https://arxiv.org/abs/2101.12722

2020

Davydov A., Marcugini S., Pambianco F., Bounds for Complete Arcs in PG(3,q) and Covering Codes of Radius 3, Codimension 4, Under a Certain Probabilistic Conjecture. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science, vol 12249, pp 107-122. Springer, Cham. http://iitp.ru/https://doi.org/10.1007/978-3-030-58799-4_8

Davydov A., Marcugini S., Pambianco F., On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4, electronic preprint arXiv:2007.08798 [cs.IT], 22 pages, 2 tables, 36 references, July 2020 http://iitp.ru/https://arxiv.org/abs/2007.08798

Davydov A., Marcugini S., Pambianco F., On integral weight spectra of the MDS codes cosets of weight 1, 2, and 3, electronic preprint, arXiv:2007.02405 [cs.IT], 12 pages, 21 references, July 2020 http://iitp.ru/https://arxiv.org/abs/2007.02405

Bartoli D., Davydov A., Marcugini S., Pambianco F., On planes through points off the twisted cubic in PG(3,q) and multiple covering codes, Finite Fields and Their Applications, vol. 67,. Oct. 2020, paper 101710. http://iitp.ru/https://doi.org/10.1016/j.ffa.2020.101710

Bartoli D., Davydov A., Marcugini S., Pambianco F., Tables, bounds and graphics of short linear codes with covering radius 3 and codimension 4 and 5, electronic preprint, arXiv:1712.07078v6 [cs.IT], 51 pages, 14 figures, 5 tables, 35 references, June 2020 http://iitp.ru/https://arxiv.org/abs/1712.07078v6

Bartoli D., Davydov A., Marcugini S., Pambianco F., On planes through points off the twisted cubic in PG(3,q) and multiple covering codes, electronic preprint, arXiv:1909.00207v2 [math.CO], 27 pages, 2 tables, 31 references, March 2020 http://arxiv.org/abs/1909.00207v2

Davydov A., Marcugini S., Pambianco F., New bounds for linear codes of covering radius 3 and 2-saturating sets in projective spaces. In: Proceedings of 2019 XVI International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY), ISBN 978-1-7281-1944-1, Moscow, Russia, 21--25 October 2019, pp. 47--52, Date Added to IEEE Xplore: 20 February 2020, DOI:10.1109/REDUNDANCY48165.2019.9003348 http://iitp.ru/https://ieeexplore.ieee.org/document/9003348

2019

Bartoli D., Davydov A., Kreshchuk A., Marcugini S., Pambianco F., New upper bounds on the smallest size of a complete cap in the spaces PG(3,q) and PG(4,q), Ars Combinatoria, vol. 147, Oct. 2019, pp. 87-96 http://www.combinatorialmath.ca/ArsCombinatoria/Vol147.html

Bartoli D., Davydov A., Marcugini S., Pambianco F., On planes through points off the twisted cubic in PG(3,q) and multiple covering codes, electronic preprint, arXiv:1909.00207v1 [math.CO], 25 pages, 2 tables, 22 references, August 2019 http://iitp.ru/https://arxiv.org/abs/1909.00207

Davydov A., Marcugini S., Pambianco F., New covering codes of radius R, codimension tR and tR+R/2, and saturating sets in projective spaces, Designs, Codes and Cryptography, 2019, Vol. 87, No. 12, pp. 2771–2792 http://iitp.ru/https://link.springer.com/article/10.1007/s10623-019-00649-2

Bartoli D., Davydov A., Marcugini S., Pambianco F., Tables, bounds and graphics of short linear codes with covering radius 3 and codimension 4 and 5, electronic publication, arXiv:1712.07078v5 [cs.IT], 49 pages, 14 figures, 5 tables, 35 references, Dec.2019 http://iitp.ru/https://arxiv.org/abs/1712.07078

Davydov A., Marcugini S., Pambianco F., New covering codes of radius R, codimension tR and tR+R/2, and saturating sets in projective spaces, electronic publication, arXiv:1808.09301v2 [math.CO], 25 pages, 1 table, 33 references, March 2019 http://iitp.ru/https://arxiv.org/abs/1808.09301

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., New bounds for linear codes of covering radii 2 and 3, Cryptography and Communications, Special Issue on Coding Theory and Applications, Vol. 11,No. 5, pp 903–920, 2019 http://iitp.ru/https://link.springer.com/article/10.1007/s12095-018-0335-0

2018

Davydov A., Faina G., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete cap in PG(N,q), N ≥3, under a certain probabilistic conjecture, Australasian Journal of Combinatorics, vol. 72, Part 3, 2018, pp. 516--535 http://iitp.ru/https://ajc.maths.uq.edu.au/pdf/72/ajc_v72_p516.pdf

Davydov A., Marcugini S., Pambianco F., New covering codes of radius R, codimension tR and tR+R/2, and saturating sets in projective spaces, electronic publication, arXiv:1808.09301v1 [math.CO], 28 pages, 1 table, 30 references, August 2018 http://iitp.ru/https://arxiv.org/abs/1808.09301

Bartoli D., Davydov A., Marcugini S., Pambianco F., On the Smallest Size of an Almost Complete Subset of a Conic in PG(2,q) and Extendability of Reed–Solomon Codes, Problems of Information Transmission, 2018, Vol. 54, No. 2, pp. 101–115 http://iitp.ru/https://rdcu.be/bKhbN

Bartoli D., Davydov A., Marcugini S., Pambianco F., Tables, bounds and graphics of short linear codes with covering radius 3 and codimension 4 and 5, electronic publication, arXiv:1712.07078v3 [cs.IT], 27 pages, 8 figures, 4 tables, 25 references, August 2018 http://iitp.ru/https://arxiv.org/abs/1712.07078

Davydov A., Marcugini S., Pambianco F., New Results on Binary Codes Obtained by Doubling Construction, , Cybernetics and Information Technologies, Vol. 18, No 5, pp. 63-76, 2018 http://www.cit.iit.bas.bg/CIT_2018/v-18-5s/07_paper.pdf

Davydov A., Marcugini S., Pambianco F., On Almost Complete Caps in PG(N, q), Cybernetics and Information Technologies, Vol. 18, No 5, pp. 54-62, 2018 http://iitp.ru/https://doi.org/10.2478/cait-2018-0020

Davydov A., Marcugini S., Pambianco F., Classification of minimal 1-saturating sets in PG(v,2), 2 ≤ v ≤ 6, electronic publication, arXiv:1802.04214[math.CO], 25 pages, 6 tables, 35 references, February 2018 http://iitp.ru/https://arxiv.org/abs/1802.04214

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tables, bounds and graphics of sizes of complete arcs in the plane PG(2,q) for all q ≤ 321007 and sporadic q in [323761 ... 430007] obtained by an algorithm with fixed order of points (FOP), electronic publication, arXiv:11404.0469[math.CO], 111 pages, 8 figures, 6 tables, 92 references, January 2018 http://iitp.ru/https://arxiv.org/abs/1404.0469

2017

Bartoli D., Davydov A., Marcugini S., Pambianco F., On Almost Complete Subsets of a Conic in PG(2, q), Completeness of Normal Rational Curves and Extendability of Reed-Solomon Codes, electronic publication, arXiv:1609.05657[math.CO], 39 pages, 2 figures, 4 tables, 23 references, December 2017 http://iitp.ru/https://arxiv.org/abs/1609.05657

Bartoli D., Davydov A., Marcugini S., Pambianco F., Tables, bounds and graphics of short linear codes with covering radius 3 and codimension 4 and 5, electronic publication, arXiv:1712.07078 [cs.IT], 22 pages, 7 figures, 2 tables, 24 references, December 2017 http://iitp.ru/https://arxiv.org/abs/1712.07078

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., New Bounds for Linear Codes of Covering Radius 2. In: Proceedings of 5th International Castle Meeting, ICMCTA 2017, Coding Theory and Applications, Vihula, Estonia, August 28–31, 2017, Angela I. Barbero, Vitaly Skachek, Oyvind Ytrehus (Eds.) pp. 1-10, Lecture Notes in Computer Science, vol. 10495, 2017, Springer, Cham http://iitp.ru/https://link.springer.com/chapter/10.1007/978-3-319-66278-7_1

Afanassiev V., Davydov A., Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4, Proceedings of 2017 IEEE International Symposium on Information Theory (ISIT), June 25--30, 2017, Aachen, Germany, pp. 2193--2197, ISBN 978-1-5090-4096-4, ISSN 2157-8117 http://ieeexplore.ieee.org/document/8006918/

Davydov A., Marcugini S., Pambianco F., Further results on binary codes obtained by doubling construction, Proceedings Eighth International Workshop on Optimal Codes and Related Topics, OC2017 (in Second International Conference “Mathematics Days in Sofia”), July 10-14, Sofia, Bulgaria, pp.73-80, 2017 http://www.math.bas.bg/moiuser/OCRT2017/a15.pdf

Davydov A., Marcugini S., Pambianco F., Upper bounds on the smallest size of an almost complete cap in PG(N,q), Proceedings Eighth International Workshop on Optimal Codes and Related Topics , OC2017 (in Second International Conference “Mathematics Days in Sofia”), July 10-14, Sofia, Bulgaria, pp. 67-72, 2017 http://www.math.bas.bg/moiuser/OCRT2017/a14.pdf

Afanassiev V., Davydov A., Zigangirov D., Estimating the Fraction of Erasure Patterns Correctable by Linear Codes, Journal of Communications Technology and Electronics, 2017, vol. 62, No. 6, pp. 669–685 http://iitp.ru/https://link.springer.com/article/10.1134/S106422691706002X

Davydov A., Faina G., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete cap in PG(N,q), N ≥ 3, under a certain probabilistic conjecture, electronic publication, arXiv:1706.01941 [math.CO], 22 pages, 42 references, 3 figures , June 2017 http://iitp.ru/https://arxiv.org/abs/1706.01941

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., Conjectural upper bounds on the smallest size of a complete cap in PG(N, q), N ≥ 3, Electronic Notes in Discrete Mathematics, vol. 57, Algebraic and Combinatorial Coding Theory, pp. 15–20, 2017 http://www.sciencedirect.com/science/article/pii/S1571065317300045

Bartoli D., Davydov A., Kreshchuk A., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete cap in PG(3, q) and PG(4, q), Electronic Notes in Discrete Mathematics, vol. 57, Algebraic and Combinatorial Coding Theory, pp. 21–26, 2017 http://www.sciencedirect.com/science/article/pii/S1571065317300057

Afanassiev V., Davydov A., Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4, electronic publication, arXiv:1703.04106v2 [cs.IT], 5 pages, 11 references, 2 tables, June 2017 http://iitp.ru/https://arxiv.org/abs/1703.04106

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., Upper bounds on the smallest size of a saturating set in projective planes and spaces of even dimension, electronic publication, arXiv:1702.07939 [math.CO], 14 pages, 34 references, 1 figure, February 2017 http://iitp.ru/https://arxiv.org/abs/1702.07939

2016

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., Conjectural upper bounds on the smallest size of a complete cap in PG(N,q), N>=3, in Proceedings XV Int. Workshop on Algebraic and Combinatorial Coding Theory, ACCT2016, Albena, Bulgaria, June 18--24, 2016, pp. 27--34.

Bartoli D., Davydov A., Kreshchuk A., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete cap in PG(3; q) and PG(4; q), in Proceedings XV Int. Workshop on Algebraic and Combinatorial Coding Theory, ACCT2016, Albena, Bulgaria, June 18--24, 2016, pp. 19--26.

Afanassiev V., Davydov A., Zigangirov D., Design and Analysis of Codes with Distance 4 and 6 Minimizing the Probability of Decoder Error,Journal of Communications Technology and Electronics, 2016, vol. 61, No. 12, pp. 1440–1455 http://link.springer.com/article/10.1134/S1064226916120020

Bartoli D., Davydov A., Kreshchuk A., Marcugini S., Pambianco F., Tables, bounds and graphics of the smallest known sizes of complete caps in the spaces PG(3,q) and PG(4,q), electronic publication, arXiv:1610.09656[math.CO], 26 pages, October 2016 http://iitp.ru/https://arxiv.org/abs/1610.09656

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., New Upper Bounds on the Smallest Size of a Saturating Set in a Projective Plane, Proceedings of 2016 XV International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY), 26-29 September 2016, Saint-Petersburg, Russia. pp. 18-22. http://ieeexplore.ieee.org/document/7779320/

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., Further results on multiple coverings of the farthest-off points, Advances in Mathematics of Communications, doi:10.3934/amc.2016030, vol. 10, no. 3, pp. 613-632, 2016 http://iitp.ru/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=12788

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search, DOI: 10.1007/s00022-015-0277-z, Journal of Geometry, vol. 107, no. 1, pp. 89-117, 2016 http://link.springer.com/article/10.1007/s00022-015-0277-z

Davydov A., Faina G., Giulietti M., Marcugini S., Pambianco F., On constructions and parameters of symmetric configurations v_k, Designs Codes Cryptography, DOI 10.1007/s10623-015-0070-x, vol. 80, no. 1, pp. 125-147, 2016 http://link.springer.com/article/10.1007/s10623-015-0070-x

2015

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tables, bounds and graphics of sizes of complete lexiarcs in the plane PG(2, q) for all q ≤ 301813 and sporadic q in the interval [301897 . . . 430007] obtained by an algorithm with fixed order of points (FOP), electronic publication, arXiv:1404.0469v2[math.CO], 114 pages, July 2015 http://arxiv.org/abs/1404.0469v2

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane PG(2,q) for all q ≤ 160001 and sporadic q in the interval [160801...430007], electronic publication, arXiv:1312.2155v3 [math.CO], 85 pages, June 2015 http://arxiv.org/abs/1312.2155v3

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., Multiple coverings of the farthest-off points with small density from projective geometry, Advances in Mathematics for Communications, vol. 9, no. 1, pp. 63-85, 2015. http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10831

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., New types of estimates for the smallest size of complete arcs in a finite Desarguesian projective plane, Journal of Geometry, 2015, vol. 106, no. 1, pp. 1-17 http://link.springer.com/article/10.1007/s00022-014-0224-4

2014

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Upper bounds on the smallest size of a complete arc in PG(2,q) under a certain probabilistic conjecture, Problems of Information Transmission, 2014, vol. 50, no. 4, pp 320-339 http://link.springer.com/article/10.1134%2FS0032946014040036

Davydov A., Faina G., Giulietti M., Marcugini S., Pambianco F., Tables of parameters of symmetric configurations v_k, electronic publication, arXiv:1312.3837v2 [math.CO], 38 pages, September 2014 http://arxiv.org/abs/1312.3837v2

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tkachenko I., Upper bounds on the smallest sizes of a complete arc in PG(2,q) based on computer search, in Proceedings XIV International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2014, Svetlogorsk , Russia, 2014,32-40 http://www.moi.math.bas.bg/acct2014/a5.pdf

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Conjectural upper bounds on the smallest size of a complete arc in PG(2,q) based on an analysis of step-by-step greedy algorithms, in Proceedings XIV International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2014, Svetlogorsk , Russia, 2014, 24-31 http://www.moi.math.bas.bg/acct2014/a4.pdf

Afanassiev V., Davydov A., Incremental calculation of decoding failure probability for iterative decoding of Reed-Solomon product code, in Proceedings XIV International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2014, Svetlogorsk , Russia, 2014, 7-13 http://www.moi.math.bas.bg/acct2014/a1.pdf

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tables of sizes of small complete arcs in the plane PG(2, q), q ≤ 410009, electronic publication, arXiv:1312.2155v2 [math.CO], 89 pages, August 2014 http://arxiv.org/abs/1312.2155

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., Tables of sizes of random complete arcs in the plane PG(2,q), electronic publication, arXiv:1405.5862 [math.CO], 37 pages, 2014 http://iitp.ru/ http://arxiv.org/abs/1405.5862

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., Tables of sizes of small complete arcs in the plane PG(2,q), q ≤ 190027, obtained by an algorithm with fixed order of points (FOP), electronic publication, arXiv:1404.0469v1 [math.CO], 66 pages, April 2014 http://arxiv.org/abs/1404.0469

2013

Davydov A., Faina G., Giulietti M., Marcugini S., Pambianco F., Tables of parameters of symmetric configurations v_k, electronic publication, arXiv:1312.3837v1 [math.CO], 36 pages, December 2013 http://arxiv.org/abs/1312.3837v1

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Tables of sizes of small complete arcs in the plane PG(2, q), q ≤ 360007, electronic publication, arXiv:1312.2155v1 [math.CO], 71 pages, December 2013 http://arxiv.org/abs/1312.2155v1

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., New upper bounds on the smallest size of a complete cap in the space PG(3,q), in Proceedings VII International Workshop on Optimal Codes and Related Topics, OC2013, Albena, Bulgaria, 2013, pp. 26–-32 http://www.moi.math.bas.bg/oc2013/a4.pdf

Bartoli D., Davydov A., Faina G., Kreshchuk A., Marcugini S., Pambianco F., Two types of upper bounds on the smallest size of a complete arc in the plane PG(2,q), in Proceedings VII International Workshop on Optimal Codes and Related Topics, OC2013, Albena, Bulgaria, 2013, pp. 19–-25 http://www.moi.math.bas.bg/oc2013/a3.pdf

Afanassiev V., Davydov A., Potapov V., Generalized concatenated coding and Fourier transform, in Proceedings VII International Workshop on Optimal Codes and Related Topics, OC2013, Albena, Bulgaria, 2013, pp. 7-12 http://www.moi.math.bas.bg/oc2013/a1.pdf

Bartoli D., Davydov A., Marcugini S., Pambianco F., A 3-cycle construction of complete arcs sharing (q+3)/2 points with a conic, Advances in Mathematics for Communications, vol. 7, no. 3, pp. 319–334, 2013. http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8818

Bartoli D., Faina G., Marcugini S., Pambianco F., Davydov A., A new algorithm and a new type of estimate for the smallest size of complete arcs in PG(2, q), Electronic Notes in Discrete Mathematics, vol. 40, Combinatorics 2012, pp. 27–31, 2013 http://www.sciencedirect.com/science/article/pii/S1571065313000073

Pambianco F., Davydov A., Bartoli D., Giulietti M., Marcugini S., A note on multiple coverings of the farthest-off points, Electronic Notes in Discrete Mathematics, vol. 40, Combinatorics 2012, pp. 289--293, 2013 http://www.sciencedirect.com/science/article/pii/S1571065313000528

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., New upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane, Journal of Geometry, vol. 104, no. 1, pp. 11-43, 2013 http://link.springer.com/article/10.1007/s00022-013-0154-6

Davydov A., Giulietti M., Marcugini S., Pambianco F., Some combinatorial aspects of constructing bipartite-graph codes, Graphs and Combinatorics, vol. 29, no. 2, pp. 187-212 (2013) http://link.springer.com/article/10.1007/s00373-011-1103-5

2012

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., On sizes of complete arcs in PG(2,q), Discrete Mathematics, vol.312 (2012) pp. 680-698. http://www.sciencedirect.com/science/article/pii/S0012365X11003104

Bartoli D., Davydov A., Giulietti M., Marcugini S., Pambianco F., Multiple coverings of the farthest-off points and multiple saturating sets in projective spaces, in Proceedings XIII International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2012, Pomorie, Bulgaria, 2012, 53-59 http://www.moi.math.bas.bg/moiuser/~ACCT2012/b9.pdf

Bartoli D., Davydov A., Faina G., Marcugini S., Pambianco F., New upper bounds on the smallest size of a complete arc in the plane PG(2,q), in Proceedings XIII International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2012, Pomorie, Bulgaria, 2012, 60-66. http://www.moi.math.bas.bg/moiuser/~ACCT2012/b10.pdf

Bartoli D., Davydov A., Marcugini S., Pambianco F., New type of estimations for the smallest size of complete arcs in PG(2,q), in Proceedings XIII International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2012, Pomorie, Bulgaria, 2012, 67-72 http://www.moi.math.bas.bg/moiuser/~ACCT2012/b11.pdf

2011

Kreshchuk A., Davydov A., Zyablov V., A.A. Kreshchuk, A.A. Davydov, and V.V. Zyablov, Codes for MIMO transmission based on orthogonal sequences, Problems of Information Transmission, vol. 47 (2011) 305--326. http://link.springer.com/article/10.1134%2FS0032946011040016

Bartoli D., Davydov A., Marcugini S., Pambianco F., The minimum order of complete caps in PG(4,4), Advances in Mathematics of Communications, vol. 5, pp. 37-40 (2011). http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5895

Davydov A., Giulietti M., Marcugini S., Pambianco F., Linear nonbinary covering codes and saturating sets in projective spaces, Advances in Mathematics of Communications, vol. 5, pp. 119-147 (2011) http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5902

2010

Davydov A., Zyablov V., Kalimullin R.E., Special sequences as subcodes of Reed--Solomon codes, Problems of Information Transmission, vol. 46 (2010) 321--345. http://link.springer.com/article/10.1134%2FS0032946010040046

Davydov A., Giulietti M., Marcugini S., Pambianco F., New inductive constructions of complete caps in PG(N,q), q even, Journal of Combinatorial Design, v. 18, 2010, pp. 176--201. http://onlinelibrary.wiley.com/doi/10.1002/jcd.20230/abstract

Davydov A., Ostergard P.R.J., Linear codes with covering radius 3, Designs Codes Cryptography, v. 54, 2010, pp. 253--271. http://iitp.ru/https://link.springer.com/article/10.1007%2Fs10623-009-9322-y

2009

Afanassiev V., Davydov A., Zyablov V., "Low density parity check codes on bipartite graphs with Reed-Solomon constituent codes" Information processes, v. 9, no. 4, 2009, pp. 301–331 http://www.jip.ru/2009/301-331-2009.pdf

Davydov A., Giulietti M., Marcugini S., Pambianco F., "On the spectrum of possible parameters of symmetric configurations." Proceedings of XII International Symposium on Problems of Redundancy in Information and Control Systems. St.-Petersburg, Russia, 2009, pp. 59-64. http://k36.org/redundancy2009

Davydov A., Giulietti M., Marcugini S., Pambianco F., "On sharply transitive sets in PG(2,q)". Innovations in Incidence Geometry, v. 6-7, 2009, pp. 139-151. http://www.iig.ugent.be/contents-6.php

Davydov A., Marcugini S., Pambianco F., "Complete (q^{2}+q+8)/2-caps in the spaces PG(3,q), q = 2 (mod 3) an odd prime, and a complete 20-cap in PG(3,5)." Designs, Codes and Cryptography, v. 50, no. 3, 2009, pp. 359-372. http://www.springerlink.com/content/xr5p07h224217k40/

Davydov A., Faina G., Marcugini S., Pambianco F., "On sizes of complete caps in projective spaces PG(n,q) and arcs in planes PG(2,q)." Journal of Geometry, v.94, no. 1-2, 2009, pp. 31-58. http://www.springerlink.com/content/03qj06133347v523/

2008

Davydov A., Faina G., Marcugini S., Pambianco F., “On the spectrum of sizes of complete caps in projective spaces PG(n,q) of small dimension,” in: Proc. XI International Workshop on Algebraic and Combinatorial Coding Theory, ACCT2008, Pamporovo, Bulgaria, 2008, pp. 57-62. http://www.moi.math.bas.bg/acct2008/b10.pdf

Davydov A., Giulietti M., Marcugini S., Pambianco F., “Linear Covering Codes of Radius 2 and 3,” in Proc. Workshop “Coding Theory Days in St. Petersburg”, St. Petersburg, Russia, Oct. 2008, pp. 12-17.

Davydov A., Giulietti M., Marcugini S., Pambianco F., “Symmetric configurations for bipartite-graph codes,” in Proc. XI International Workshop Algebraic Combinatorial Coding Theory, ACCT2008, Pamporovo, Bulgaria, Jun. 2008, pp. 63-69. http://www.moi.math.bas.bg/acct2008/b11.pdf

Davydov A., M. Giulietti , Marcugini S., Pambianco F., “Linear covering codes over nonbinary finite fields,” in Proceedings of XI International Workshop on Algebraic and Combintorial Coding Theory, ACCT2008, Pamporovo, Bulgaria, Jun. 2008, pp. 70-75. http://www.moi.math.bas.bg/acct2008/b12.pdf

2007

Afanassiev V., Davydov A., Zyablov V., “Low density concatenated codes with Reed-Solomon component codes,” in Proc. XI International Symposium on Problems of Redundancy in Information and Control Systems, Saint-Petersburg, Russia, July, 2007, pp. 47-51. http://k36.org/redundancy2007/proceedings.php

Davydov A., Giulietti M., Marcugini S., F. Pambianco , “New constructions of small complete caps in PG(N,q), q even,” in Proc. XI International Symposium on Problems of Redundancy in Information and Control Systems, Saint-Petersburg, Russia, July, 2007, pp. 213-217. http://k36.org/redundancy2007/proceedings.php

2006

Davydov A., Marcugini S., F. Pambianco , “Complete (q²+q+8)/2-caps in the projective space PG(3,q) with odd prime q ≡ 2 (mod 3),” in: Proc. X International Workshop on Algebraic and Combinatorial Coding Theory, ACCT-X, Zvenigorod, Russia, Sept. 2006, pp. 76-80.

Davydov A., Marcugini S., Pambianco F., “Minimal 1-saturating sets and complete caps in binary projective spaces,” Journal Combinatorial Theory, Ser. A, vol. 113, 2006, pp. 647-663. http://www.sciencedirect.com/science/article/pii/S009731650500107X

2005

Davydov A., Faina G., S. Marcugini , Pambianco F., "Locally optimal covering codes and minimal saturating sets," in Proceedings of Fourth Int. Workshop on Optimal Codes and Related Topics, OC2005, Pamporovo, Bulgaria, June 17-23, pp. 114-120, 2005.

Davydov A., Faina G., Marcugini S., F. Pambianco , "Computer search in projective planes for the sizes of complete arcs," Journal of Geometry, vol. 82, pp. 50-62, 2005. http://link.springer.com/article/10.1007/s00022-004-1719-1

Davydov A., Faina G., F. Pambianco , "Constructions of small complete caps in binary projective spaces," Designs, Codes and Cryptography, vol. 37, pp. 61-80, 2005. http://link.springer.com/article/10.1007%2Fs10623-004-3805-7

Davydov A., Faina G., Marcugini S., Pambianco F., "Locally optimal (nonshortening) linear covering codes and minimal saturating sets in projective spaces," IEEE Transactions on Information Theory, vol. 51, No. 12, pp. 4378-4387, 2005. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1542432

2004

Afanassiev V., Davydov A., Podzorov S.V., "Some hints on implementation of soft Sudan decoding," in: Proceedings of the Ninth International Workshop on Algebraic and Combinatorial Coding Theory, ACCT-IX, pp. 7-13, Kranevo, Bulgaria, June 19-25, 2004.

Davydov A., Marcugini S., Pambianco F., "Minimal 1-saturating sets and complete caps in binary projective geometries," in: Proceedings of the Ninth International Workshop on Algebraic and Combinatorial Coding Theory, ACCT-IX, pp. 113-119, Kranevo, Bulgaria, June 19-25, 2004.

Davydov A., Marcugini S., Pambianco F., "Complete caps in projective spaces PG(n,q)," Journal of Geometry, vol. 80, pp. 23-30, 2004. http://link.springer.com/article/10.1007/s00022-004-1778-3

Davydov A., Marcugini S., Pambianco F., "Linear Codes with Covering Radius 2,3 and Saturating Sets in Projective Geometry," IEEE Transactions on Information Theory, vol. 50, No. 3, pp. 537-541, 2004. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1273664

2003

Davydov A., Marcugini S., Pambianco F., "On Saturating Sets in Projective Spaces," Journal of Combinatorial Theory, Series A, vol. 103, pp. 1-15, 2003. http://www.sciencedirect.com/science/article/pii/S0097316503000529

2002

Afanassiev V., Davydov A., "Finite field towers: iterated presentation and complexity of arithmetic," Finite Fields and their Applications, vol. 8, pp. 216-232, 2002. http://www.sciencedirect.com/science/article/pii/S1071579701903375

2001

Davydov A., Östergård P.R.J., "Recursive constructions of complete caps," Journal of Statistic and Planning Inference, vol. 95, pp. 163-173, 2001. http://www.sciencedirect.com/science/article/pii/S037837580000286X

Davydov A., Östergård P.R.J., "Linear codes with covering radius R = 2,3 and codimension tR," IEEE Transactions on Information Theory, vol. 47, pp. 416-421, 2001. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=904551

Davydov A., "New constructions of covering codes," Designs, Codes and Cryptography, vol. 22, pp. 305-316, 2001. http://link.springer.com/article/10.1023/A:1008302507816

2000

Afanassiev V., Davydov A., "On iterated presentation for infinity towers of extended finite fields," in Proceedings of the Seventh International Workshop on Algebraic and Combinatorial Coding Theory, ACCT-VII, pp. 7-10, Bansko, Bulgaria, 2000.

Davydov A., Östergård P.R.J., "New quaternary linear codes with covering radius 2," Finite Fields and their Applications, vol. 6, pp. 164-174, 2000. http://www.sciencedirect.com/science/article/pii/S107157979990271X

Davydov A., Östergård P.R.J., "On saturating sets in small projective geometries," European Journal of Combinatorics, vol. 21, pp. 563-570, 2000. http://www.sciencedirect.com/science/article/pii/S0195669899903736

1999

Davydov A., Ostergard P.R.J., "New linear codes with covering radius 2 and odd basis," Designs, Codes and Cryptography, vol. 16, pp. 29-39, 1999. http://link.springer.com/article/10.1023%2FA%3A1008370224461

Davydov A., "Constructions and Families of Nonbinary Linear Codes with Covering Radius 2," IEEE Transactions on Information Theory, vol. 45, no. 5, pp.1679--1686, 1999. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=771244

1997

Davydov A., "Constructions of Nonlinear Covering Codes," IEEE Transactions on Information Theory, vol. 43, no. 5, pp. 1639--1647, 1997. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=623166

1995

Davydov A., "Constructions and families of covering codes and saturated sets of points in projective geometry,"" IEEE Transactions on Information Theory, vol. 41, no. 6, pp. 2071--2080, 1995. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=476339

1994

Davydov A., Drozhzhina--Labinskaya A.Yu., "Constructions, families and tables of binary linear covering codes,"" IEEE Transactions on Information Theory, vol. 40, no. 4, pp. 1270--1279, 1994. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=335937

1991

Gabidulin E.M., Davydov A., Tombak L.M., "Linear codes with covering radius 2 and other new covering codes,"" IEEE Transactions on Information Theory, vol. 37, no. 1, pp. 219--224, 1991. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=61146

Davydov A., Tombak L.M., "An Alternative to the Hamming Code in the Class of SEC-DED Codes in Semiconductor Memory," IEEE Transactions on Information Theory, vol. 37, no. 3, part II, pp. 897-902, 1991. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=79958

1990

Davydov A., "Constructions of linear covering codes," Problems of Information Transmission, vol. 26, no. 4, pp. 317--331, 1990. http://www.pit-contents.iitp.ru/4-90.html

1989

Davydov A., M. Tombak L., “Quasi-perfect linear binary codes with distance 4 and complete caps in projective geometry," Problems of Information Transmission, vol. 25, no. 4, pp. 265--275, 1989. http://www.pit-contents.iitp.ru/4-89.html

1987

Boyarinov I.M., Davydov A., Shabanov B.M., Error correction in main memory of a high-capacity computer, Automation and Remote Control, vol. 48, no.7. pt. 2, pp. 956--965, 1987

1981

Davydov A., L.N. Kaplan, Yu.B. Smerkis, Tauglikh, G.L., "Optimization of shortened Hamming codes," Problems of Information Transmission, vol. 17, no. 4, pp. 261-267, 1981. http://www.pit-contents.iitp.ru/4-81.html