New bounds for covering codes of radius 3 and codimension 3t+1. Advances in Mathematics of Communications. 14 pages, doi: 10.3934/amc.2023042 Go to publication
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 Go to publication
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 Go to publication
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 Go to publication
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
Go to publication
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 Go to publication
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 Go to publicationDownload (313.9 KB)
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 Go to publicationDownload (308.4 KB)
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 Go to publication
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 Go to publicationDownload (658.9 KB)
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 Go to publication
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 Go to publicationDownload (315.9 KB)
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 Go to publicationDownload (319.9 KB)
Twisted cubic and orbits of lines in PG(3,q), electronic preprint, arXiv:2103.12655v2 [math.CO], 27 pages, 19 references, Mar. 2021
Go to publicationDownload (277.8 KB)
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 Go to publicationDownload (239.8 KB)
On the weight distribution of the cosets of MDS codes, electronic preprint,
arXiv:2101.12722 [cs.IT], 32 pages, 45 references, June. 2021 Go to publicationDownload (375.1 KB)
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. Go to publication
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 Go to publicationDownload (253.1 KB)
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 Go to publicationDownload (152.6 KB)
2020 year
Authors: 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. Go to publication
2020 year
Authors: 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 Go to publicationDownload (1.2 MB)
2020 year
Authors: 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 Go to publicationDownload (296.4 KB)
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
Go to publication
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 Go to publication
2019 year
Authors: 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 Go to publicationDownload (264.7 KB)
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 Go to publication
2019 year
Authors: 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 Go to publicationDownload (1.2 MB)
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 Go to publicationDownload (301.7 KB)
2019 year
Authors: 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 Go to publication
2018 year
Authors: 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 Go to publicationDownload (345.2 KB)
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 Go to publicationDownload (368.4 KB)
2018 year
Authors: 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 Go to publicationDownload (314.3 KB)
2018 year
Authors: 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 Go to publicationDownload (631.1 KB)
New Results on Binary Codes Obtained by Doubling Construction, , Cybernetics and Information Technologies, Vol. 18, No 5, pp. 63-76, 2018 Go to publicationDownload (507.6 KB)
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 Go to publicationDownload (188.7 KB)
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 Go to publicationDownload (1.5 MB)
2017 year
Authors: 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 Go to publicationDownload (569.7 KB)
2017 year
Authors: 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 Go to publicationDownload (555 KB)
2017 year
Authors: 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 Go to publicationDownload (169.9 KB)
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 Go to publicationDownload (237.1 KB)
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 Go to publicationDownload (157.9 KB)
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 Go to publicationDownload (145.7 KB)
Estimating the Fraction of Erasure Patterns Correctable
by Linear Codes, Journal of Communications Technology and Electronics, 2017, vol. 62, No. 6, pp. 669–685 Go to publicationDownload (510.2 KB)
2017 year
Authors: 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 Go to publicationDownload (293 KB)
2017 year
Authors: 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 Go to publicationDownload (236.5 KB)
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 Go to publicationDownload (235.5 KB)
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 Go to publicationDownload (123.3 KB)
2017 year
Authors: 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 Go to publicationDownload (295.7 KB)