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Krotov Denis Stanislavovich

Total publications: 59 (58)
in MathSciNet: 52 (51)
in zbMATH: 43 (43)
in Web of Science: 38 (37)
in Scopus: 25 (24)
Cited articles: 42
Citations in Math-Net.Ru: 111
Citations in Web of Science: 139
Citations in Scopus: 52
Presentations: 2

Number of views:
This page:2945
Abstract pages:3646
Full texts:831
References:335
Krotov Denis Stanislavovich
Professor of Russian Academy of Sciences
Doctor of physico-mathematical sciences (2011)
Speciality: 01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date: 8.10.1974
Phone: +7 (383) 363 46 25, +7 (913) 933 14 14
E-mail:
Keywords: combinatorics, perfect codes, n-ary quasigroups, latin hypercubes.
UDC: 519.143, 621.391.15, 519.72, 519.2, 621.391, 519.173.1, 519.7

Subject:

Study of perfect codes, combinatorial aspects of n-ary quasigroups (latin hypercubes).

Biography

1981–1989 — Novosibirsk school 190, class 1v-8v
1989–1991 — Novosibirsk school 25 (gymnasium 3) 10ex-11ex
1991–1995 — Novosibirsk State University, Mech.-Math. Fac.
1995–1997 — Novosibirsk State University, Mech.-Math. Fac., master courses
1997–2000 — Sobolev Institute of Mathematics, PhD
2001–… — Sobolev Institute of Mathematics, senior reseacher, leading reseacher

   
Main publications:
  1. D. S. Krotov, “Perfect Codes in Doob Graphs”, Designs, Codes and Cryptography, 80:1 (2016), 91–102 , arXiv: 1407.6329  crossref  mathscinet  zmath  isi  elib  scopus
  2. D. S. Krotov, “On Calculation of the Interweight Distribution of an Equitable Partition”, Journal of Algebraic Combinatorics, 40:2 (2014), 373–386 , arXiv: 1303.0002  crossref  mathscinet  zmath  isi  elib  scopus
  3. D. S. Krotov, “On Weight Distributions of Perfect Colorings and Completely Regular Codes”, Designs, Codes and Cryptography, 61:3 (2011), 315–329 , arXiv: 0907.0001  crossref  mathscinet  zmath  isi  elib
  4. D. S. Krotov, P. R. J. Östergård, O. Pottonen, “On Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$”, IEEE Transactions on Information Theory, 57:10 (2011), 6771–6779 , arXiv: 1104.4013  crossref  mathscinet  isi  elib
  5. D. S. Krotov, V. N. Potapov, “$n$-Ary Quasigroups of Order $4$”, SIAM Journal on Discrete Mathematics, 23:2 (2009), 561–570 , arXiv: math/0701519  crossref  mathscinet  zmath  isi  elib
  6. D. S. Krotov, “$Z_4$-linear perfect codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 78–90 , arXiv: 0710.0198 (English translation at http://arxiv.org/abs/0710.0198)  mathnet  mathscinet  zmath  elib

http://www.mathnet.ru/eng/person29456
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:krotov.denis-s
https://mathscinet.ams.org/mathscinet/MRAuthorID/620515
http://elibrary.ru/author_items.asp?spin=3774-8396
http://orcid.org/0000-0002-8516-755X
http://www.researcherid.com/rid/L-2862-2013
http://www.scopus.com/authid/detail.url?authorId=14050575000
https://arxiv.org/a/krotov_d_1

Full list of publications:
| by years | by types | by times cited | scientific publications | common list |



   2019
1. M. Shi, D. Huang, D. Krotov, “Additive perfect codes in Doob graphs”, Designs, Codes and Cryptography, 2019 (to appear) , arXiv: 1806.04834

   2018
2. D. S. Krotov, “On the gaps of the spectrum of volumes of trades”, Journal of Combinatorial Designs, 26:3 (2018), 119–126  crossref  mathscinet  zmath  isi  elib  scopus
3. D. S. Krotov, E. A. Bespalov, “Distance-2 MDS codes and latin colorings in the Doob graphs”, Graphs and Combinatorics, 34:5 (2018), 1001–1017 , arXiv: 1510.01429  crossref  mathscinet  isi  elib  scopus
4. D. S. Krotov, The existence of perfect codes in Doob graphs, 2018 (Published online) , 6 pp., submitted, arXiv: 1810.03772
5. E. Ghorbani, S. Kamali, G. B. Khosrovshahi, D. S. Krotov, On the volumes and affine types of trades, 2018 (Published online) , 29 pp., submitted, arXiv: 1810.02296
6. M. Shi, D. Krotov, P. Solé, A new approach to the Kasami codes of type 2, 2018 (Published online) , 11 pp., in preparation, arXiv: 1810.00015
7. M. Shi, R. Wu, D. S. Krotov, On $Z_pZ_p^k$-additive codes and their duality, 2018 (Published online) , 15 pp., submitted, arXiv: 1809.00008
8. M. Shi, D. S. Krotov, P. Solé, A new distance-regular graph of diameter 3 on 1024 vertices, 2018 (Published online) , 15 pp., submitted, arXiv: 1806.07069
9. M. Shi, L. Xu, D. S. Krotov, The number of the non-full-rank Steiner triple systems, 2018 (Published online) , 13 pp., submitted, arXiv: 1806.00009

   2017
10. D. S. Krotov, “On the Automorphism Groups of the $Z_2 Z_4$-Linear $1$-Perfect and Preparata-Like Codes”, Designs, Codes and Cryptography, 83:1 (2017), 169–177 , arXiv: 1602.00036  crossref  mathscinet  zmath  isi  elib  scopus
11. E. A. Bespalov, D. S. Krotov, “MDS codes in Doob graphs”, Problems of Information Transmission, 53:2 (2017), 136–154  mathnet  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus (cited: 1)
12. D. S. Krotov, “The extended 1-perfect trades in small hypercubes”, Discrete Mathematics, 340:10 (2017), 2559–2572 , arXiv: 1512.03421  crossref  mathscinet  zmath  isi  elib  scopus
13. D. S. Krotov, “The minimum volume of subspace trades”, Discrete Mathematics, 340:12 (2017), 2723–2731 , arXiv: 1512.02592  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 1)

   2016
14. D. S. Krotov, “Perfect Codes in Doob Graphs”, Designs, Codes and Cryptography, 80:1 (2016), 91–102 , arXiv: 1407.6329  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 1)
15. D. S. Krotov, P. R. J. Östergård, O. Pottonen, “Non-Existence of a Ternary Constant Weight (16,5,15;2048) Diameter Perfect Code”, Advances in Mathematics of Communications, 10:2 (2016), 393–399 , arXiv: 1408.6927  crossref  mathscinet  zmath  isi  elib  scopus
16. D. S. Krotov, I. Yu. Mogilnykh, V. N. Potapov, “To the Theory of $q$-ary Steiner and Other-Type Trades”, Discrete Mathematics, 339:3 (2016), 1150–1157 , arXiv: 1412.3792  crossref  mathscinet (cited: 2)  zmath  isi (cited: 9)  elib  scopus (cited: 8)
17. E. A. Bespalov, D. S. Krotov, “On one test for the switching separability of graphs modulo $q$”, Siberian Mathematical Journal, 57:1 (2016), 7–17  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
18. D. S. Krotov, V. N. Potapov, “Constructions of Transitive Latin Hypercubes”, European Journal of Combinatorics, 54 (2016), 51–64 , arXiv: 1303.0004  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
19. S. V. Avgustinovich, D. S. Krotov, A. Yu. Vasil'eva, “Completely regular codes in the infinite hexagonal grid”, Sib. elektron. matem. izv., 13 (2016), 987–1016 , arXiv: 1612.01360  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
20. D. S. Krotov, A. Yu. Vasileva, “On Perfect Codes That Do Not Contain Preparata-like Codes”, Problems of Information Transmission, 52:3 (2016), 284–288 , arXiv: 1512.03048  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
21. E. V. Konstantinova, D. S. Krotov, A. D. Mednykh, “On Graphs and Groups, Spectra and Symmetries held on August 15–28, 2016, Novosibirsk, Russia”, Sib. elektron. matem. izv., 13 (2016), 1369–1382  mathnet  crossref  mathscinet  isi  elib  scopus

   2015
22. D. S. Krotov, M. Villanueva, “Classification of the $Z_2Z_4$-Linear Hadamard Codes and Their Automorphism Groups”, IEEE Transactions on Information Theory, 61:2 (2015), 887–894 , arXiv: 1408.1147  crossref  mathscinet (cited: 1)  isi (cited: 3)  elib  scopus (cited: 4)
23. D. S. Krotov, E. V. Sotnikova, “Embedding in $q$-ary $1$-Perfect Codes and Partitions”, Discrete Mathematics, 338:11 (2015), 1856–1859 , arXiv: 1412.3795  crossref  mathscinet  zmath  isi  elib (cited: 1)  scopus (cited: 1)
24. D. S. Krotov, “On the Number of Maximum Independent Sets in Doob Graphs”, Siberian Electronic Mathematical Reports, 12 (2015), 508–512 , arXiv: 1612.00007  mathnet  crossref  zmath  elib  scopus (cited: 2)
25. J. I. Kokkala, D. S. Krotov, P. R. J. Östergård, “On the Classification of MDS Codes”, IEEE Transactions on Information Theory, 61:12 (2015), 6485–6492 , arXiv: 1411.5822  crossref  mathscinet (cited: 3)  isi (cited: 7)  elib  scopus (cited: 8)

   2014
26. D. S. Krotov, “A Partition of the Hypercube into Maximally Nonparallel Hamming Codes”, Journal of Combinatorial Designs, 22:4 (2014), 179–187 , arXiv: 1210.0010  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
27. D. S. Krotov, V. N. Potapov, “Propelinear 1-Perfect Codes from Quadratic Functions”, IEEE Transactions on Information Theory, 60:4 (2014), 2065–2068 , arXiv: 1301.0014  crossref  mathscinet (cited: 2)  isi (cited: 3)  elib (cited: 3)  scopus (cited: 3)
28. D. S. Krotov, “On Calculation of the Interweight Distribution of an Equitable Partition”, Journal of Algebraic Combinatorics, 40:2 (2014), 373–386 , arXiv: 1303.0002  crossref  mathscinet  zmath  isi  elib  scopus

   2015
29. K. V. Vorob'ev, D. S. Krotov, “Bounds for the Size of a Minimal 1-Perfect Bitrade in a Hamming Graph”, Journal of Applied and Industrial Mathematics, 9:1 (2015), 141–146  mathnet  crossref  mathscinet (cited: 2)  mathscinet (cited: 2)  zmath  elib  elib  scopus (cited: 3)

   2013
30. H. K. Kim, D. S. Krotov, J. Y. Lee, “Matrices Uniquely Determined by Their Lonesums”, Linear Algebra and its Applications, 438:7 (2013), 3107–3123 , arXiv: 1103.4884  crossref  mathscinet  zmath  isi (cited: 1)  elib

   2012
31. D. S. Krotov, “On the Binary Codes with Parameters of Triply-Shortened 1-Perfect Codes”, Designs, Codes and Cryptography, 64:3 (2012), 275–283 , arXiv: 1104.0005  crossref  mathscinet (cited: 2)  zmath  isi (cited: 3)  elib

   2011
32. V. N. Potapov, D. S. Krotov, “On the number of $n$-ary quasigroups of finite order”, Discrete Mathematics and Applications, 21:5-6 (2011), 575–585 , arXiv: 0912.5453  mathnet  crossref  crossref  mathscinet  zmath  elib  elib
33. D. S. Krotov, V. N. Potapov, “On Connection Between Reducibility of an $n$-Ary Quasigroup and That of Its Retracts”, Discrete Mathematics, 311:1 (2011), 58–66 , arXiv: 0801.0055  crossref  mathscinet (cited: 2)  zmath  isi (cited: 2)  elib (cited: 4)
34. D. S. Krotov, “On Weight Distributions of Perfect Colorings and Completely Regular Codes”, Designs, Codes and Cryptography, 61:3 (2011), 315–329 , arXiv: 0907.0001  crossref  mathscinet (cited: 6)  zmath  isi (cited: 9)  elib
35. O. Heden, D. S. Krotov, “On the Structure of Non-Full-Rank Perfect $q$-Ary Codes”, Advances in Mathematics of Communications, 5:2, A special issue ALCOMA'10 (2011), 149–156 , arXiv: 1001.0001  crossref  mathscinet (cited: 4)  zmath  isi (cited: 6)  elib (cited: 6)
36. D. S. Krotov, P. R. J. Östergård, O. Pottonen, “On Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$”, IEEE Transactions on Information Theory, 57:10 (2011), 6771–6779 , arXiv: 1104.4013  crossref  mathscinet (cited: 6)  isi (cited: 3)  elib (cited: 3)

   2010
37. D. S. Krotov, “On the Binary Codes with Parameters of Doubly-Shortened $1$-Perfect Codes”, Designs, Codes and Cryptography, 57:2 (2010), 181–194 , arXiv: 0907.0002  crossref  mathscinet (cited: 6)  zmath  isi (cited: 7)  elib (cited: 8)

   2011
38. D. S. Krotov, “On connection between the switching separability of a graph and its subgraphs”, Journal of Applied and Industrial Mathematics, 5:2 (2011), 240–246 , arXiv: 1104.0003  mathnet  crossref  mathscinet  zmath  elib  elib

   2010
39. D. S. Krotov, V. N. Potapov, “On switching equivalence of $n$-ary quasigroups of order 4 and perfect binary codes”, Problems Inform. Transmission, 46:3 (2010), 219–224  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  scopus (cited: 3)

   2009
40. D. S. Krotov, V. N. Potapov, “$n$-Ary Quasigroups of Order $4$”, SIAM Journal on Discrete Mathematics, 23:2 (2009), 561–570 , arXiv: math/0701519  crossref  mathscinet (cited: 9)  zmath  isi (cited: 14)  elib (cited: 16)
41. S. V. Avgustinovich, D. S. Krotov, “Embedding in a Perfect Code”, Journal of Combinatorial Designs, 17:5 (2009), 419–423 , arXiv: 0804.0006  crossref  mathscinet (cited: 3)  zmath  isi (cited: 4)  elib (cited: 4)

   2008
42. D. S. Krotov, S. V. Avgustinovich, “On the Number of $1$-Perfect Binary Codes: A Lower Bound”, IEEE Transactions on Information Theory, 54:4 (2008), 1760–1765 , arXiv: math/0608278  crossref  mathscinet (cited: 6)  isi (cited: 6)  elib (cited: 7)
43. D. S. Krotov, V. N. Potapov, P. V. Sokolova, “On Reconstructing Reducible $n$-Ary Quasigroups and Switching Subquasigroups”, Quasigroups and Related Systems, 16:1 (2008), 55–67 , arXiv: math/0608269  crossref  mathscinet (cited: 6)  zmath
44. D. S. Krotov, “On Diameter Perfect Constant-Weight Ternary Codes”, Discrete Mathematics, 308:14 (2008), 3104–3114 , arXiv: math/0509620  crossref  mathscinet (cited: 1)  zmath  isi (cited: 1)  elib (cited: 1)
45. D. S. Krotov, “On Reducibility of $n$-Ary Quasigroups”, Discrete Mathematics, 308:22 (2008), 5289–5297 , arXiv: math/0607284  crossref  mathscinet (cited: 5)  zmath  isi (cited: 5)  elib (cited: 8)
46. D. S. Krotov, “On Decomposability of $4$-ary Distance $2$ MDS Codes, Double-Codes, and $n$-Quasigroups of Order $4$”, Discrete Mathematics, 308:15 (2008), 3322–3334 , arXiv: math/0509358  crossref  mathscinet (cited: 4)  zmath  isi (cited: 3)  elib (cited: 4)
47. D. S. Krotov, “On Irreducible $n$-Ary Quasigroups with Reducible Retracts”, European Journal of Combinatorics, 29:2 (2008), 507–513 , arXiv: math/0607785  crossref  mathscinet (cited: 5)  zmath  isi (cited: 3)  elib (cited: 7)
48. H. K. Kim, D. S. Krotov, “The Poset Metrics That Allow Binary Codes of Codimension $m$ to Be $m$-, $(m-1)$-, or $(m-2)$-Perfect”, IEEE Transactions on Information Theory, 54:11 (2008), 5241–5246 , arXiv: 0705.2807  crossref  mathscinet (cited: 3)  isi (cited: 5)  elib (cited: 2)
49. D. S. Krotov, “On perfect colorings of the halved 24-cube”, Diskretn. Anal. Issled. Oper., 15:5 (2008), 35–46 , arXiv: 0803.0068 (English translation at http://arxiv.org/abs/0803.0068)  mathnet  mathscinet  zmath  elib

   2009
50. Yu. L. Vasil'ev, S. V. Avgustinovich, D. S. Krotov, “On shifting sets in the binary hypercube”, Journal of Applied and Industrial Mathematics, 3:2 (2009), 290–296  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

   2007
51. D. S. Krotov, “$Z_{2^k}$-Dual Binary Codes”, IEEE Transactions on Information Theory, 53:4 (2007), 1532–1537 , arXiv: math/0509325  crossref  mathscinet (cited: 1)  zmath  isi (cited: 5)  elib (cited: 2)

   2006
52. V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order 4”, Siberian Mathematical Journal, 47:4 (2006), 720–731 , arXiv: math/0605104  mathnet  crossref  mathscinet  zmath  isi (cited: 14)  elib (cited: 13)  elib (cited: 13)  scopus (cited: 17)

   2004
53. D. S. Krotov, V. N. Potapov, “On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes”, Problems of Information Transmission, 40:1 (2004), 5–12  mathnet  crossref  mathscinet  zmath

   2001
54. D. S. Krotov, “$Z_4$-Linear Hadamard and Extended Perfect Codes”, WCC2001, International Workshop on Coding and Cryptography (Paris, France, 8-12 January 2001), Electronic Notes in Discrete Mathematics, 6, eds. D. Augot, C. Carlet, Elsevier B. V., 2001, 107–112 , arXiv: 0710.0199  crossref  mathscinet (cited: 7)  zmath  elib (cited: 9)
55. D. S. Krotov, “Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3”, Problems of Information Transmission, 37:1 (2001), 1–9  mathnet  crossref  mathscinet  zmath

   2000
56. D. S. Krotov, “$Z_4$-linear perfect codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 78–90 , arXiv: 0710.0198 (English translation at http://arxiv.org/abs/0710.0198)  mathnet  mathscinet  zmath  elib
57. D. S. Krotov, “Lower bounds for the number of $m$-quasigroups of order four and of the number of perfect binary codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:2 (2000), 47–53  mathnet  mathscinet  zmath  elib
58. D. S. Krotov, “On a perfect code that contains a given set of perfect codes as subcodes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:1 (2000), 40–48  mathnet  mathscinet  zmath  elib
59. D. S. Krotov, “Combining Construction of Perfect Binary Codes”, Problems of Information Transmission, 36:4 (2000), 349–353  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. On the classification of the equitable partitions of the 12-cube with the quotient matrix [[0,12],[4,8]]
D. S. Krotov
2018-ary quasigroups and related topics
September 21, 2018
2. Совершенные комбинаторные структуры
D. S. Krotov

June 14, 2016 14:05   

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