А.А. Давыдов - Публикации

2016

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.
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
Афанасьев В.Б., Давыдов А.А., Зигангиров Д.К., Построение и анализ кодов с расстоянием 4 и 6, минимизирующих вероятность ошибки декодера, журнал "Информационные процессы", том 16, № 1, стр. 41–60, Март 2016 http://www.jip.ru/2016/41-60-2016.pdf
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 plane arc, 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

Давыдов А.А., Davydov M.A., К вопросу о концентрации землеустройства в ходе аграрной реформы Столыпина 1907-1915 гг., Материалы XIII международной конференции Ассоциации «История и компьютер». Информационный бюллетень АИК. №38, сс. 47-48, сентябрь 2012. М. http://elibrary.ru/item.asp?id=17912378
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

Крещук А.А., Давыдов А.А., Зяблов В.В., Коды для многоантенной передачи и приема на основе ортогональных последовательностей, Проблемы передачи информации, т. 47, вып. 4, сс. 3–26 (2011) 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

Давыдов А.А., Зяблов В.В., Калимуллин Р.Э., Специальные последовательности как подкоды кода Рида–Соломона, Проблемы передачи информации, 2010, т. 46, вып. 4, сc. 56–82 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://www.springerlink.com/content/w2442kk317020434/

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. http://iitp.ru/ http://k36.org/codingdays/proceedings.pdf
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

Грошев Ф.В., Давыдов А.А., «Декодер кодов Рида-Соломона» // в сборнике трудов 30-й конференции молодых ученых и специалистов ИППИ РАН «Информационные технологии и системы», Звенигород, Россия, 18-21 сентября, 2007 г., стр.77-80, ISBN 978-5-7834-0193-0
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

Афанасьев В.Б., Давыдов А.А., "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