Persons: Krotov, Denis Stanislavovich

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Krotov, Denis Stanislavovich

Statistics
in MathSciNet:	87 (86)
in zbMATH:	81 (81)
in Web of Science:	78 (77)
in Scopus:	89 (88)

Professor of Russian Academy of Sciences

Doctor of physico-mathematical sciences (2011)

Speciality:

01.01.09 (Discrete mathematics and mathematical cybernetics)

E-mail:

Keywords:

combinatorics, completely regular codes, equitable partitions, 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); any other combinatorial configurations that can be represented as completely regular codes or equitable partitions

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 researcher, ..., chief researcher

Main publications:

D. S. Krotov, “Perfect Codes in Doob Graphs”, Designs, Codes and Cryptography, 80:1 (2016), 91–102 https://rdcu.be/6gzd, arXiv: 1407.6329
D. S. Krotov, “On Calculation of the Interweight Distribution of an Equitable Partition”, Journal of Algebraic Combinatorics, 40:2 (2014), 373–386 https://rdcu.be/dJ8wb, arXiv: 1303.0002
D. S. Krotov, “On Weight Distributions of Perfect Colorings and Completely Regular Codes”, Designs, Codes and Cryptography, 61:3 (2011), 315–329 https://rdcu.be/dJ8wf, arXiv: 0907.0001
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
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
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)

https://www.mathnet.ru/eng/person29456

List of publications on Google Scholar

https://zbmath.org/authors/ai:krotov.denis-s

https://mathscinet.ams.org/mathscinet/MRAuthorID/620515

https://elibrary.ru/author_items.asp?authorid=17861

https://orcid.org/0000-0002-8516-755X

https://www.webofscience.com/wos/author/record/L-2862-2013

https://www.scopus.com/authid/detail.url?authorId=14050575000

https://www.researchgate.net/profile/Denis_Krotov

https://arxiv.org/a/krotov_d_1

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2026
1.	M. Shi, X. Li, D. S. Krotov, “Triangle decompositions of PG$(n-1,2)$”, Discrete Mathematics, 349:1 (2026), 114664 , 13 pp., arXiv: 2407.19157

2025
2.	E. A. Bespalov, D. S. Krotov, “On extended 1-perfect bitrades”, Discrete Mathematics, 348:1 (2025), 114222 , 12 pp., arXiv: 2012.02183
3.	D. S. Krotov, V. N. Potapov, “Completely Regular Codes and Equitable Partitions”, Chapter 1, Completely Regular Codes in Distance Regular Graphs, eds. M. Shi, P. Solé, CRC Press, 2025, 1–84
4.	E. A. Bespalov, D. S. Krotov, “Some Completely Regular Codes in Doob Graphs”, Chapter 6, Completely Regular Codes in Distance Regular Graphs, eds. M. Shi, P. Solé, CRC Press, 2025, 379–448
5.	J. H. Koolen, D. S. Krotov, W. J. Martin, “Completely Regular Codes: Tables of Small Parameters for Binary and Ternary Hamming Graphs”, Chapter 7, Completely Regular Codes in Distance Regular Graphs, eds. M. Shi, P. Solé, CRC Press, 2025, 449–502
6.	D. S. Krotov, I. Yu. Mogilnykh, “Multispreads”, Finite Fields and Their Applications, 108 (2025), 102675 , 25 pp., arXiv: 2312.07883
7.	D. S. Krotov, F. Özbudak, V. N. Potapov, “Generalizing the Bierbrauer–Friedman bound for orthogonal arrays”, Designs, Codes and Cryptography, 93:11 (2025), 4937–4950 https://rdcu.be/eCtdH, arXiv: 2411.16559

2024
8.	D. S. Krotov, V. N. Potapov, “An upper bound on the number of frequency hypercubes”, Discrete Mathematics, 347:1 (2024), 113657 , 9 pp., arXiv: 2212.00048
9.	M. Shi, D. S. Krotov, F. Özbudak, “Constructing MRD codes by switching”, Journal of Combinatorial Designs, 32:5 (2024), 219–237 https://onlinelibrary.wiley.com/share/author/ZZBCUZ2BDVAVQKCBKXTN?target=10.1002/jcd.21931, arXiv: 2211.00298	2 ^[x]
10.	D. S. Krotov, “The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes”, Discrete Mathematics, 347:5 (2024), 113923 , 8 pp., arXiv: 2311.05428
11.	D. S. Krotov, “Equitable [[2,10],[6,6]]-Partitions of the 12-Cube”, Cryptography and Communications, 16:5 (2024), 975–996 https://rdcu.be/dFVoy, arXiv: 2012.00038	1 ^[x]
12.	D. S. Krotov, “Multifold 1-Perfect Codes”, Journal of Combinatorial Designs, 32:9 (2024), 546–555 https://onlinelibrary.wiley.com/share/author/ES6FTKN28B59JMBJGI5N?target=10.1002/jcd.21947, arXiv: 2212.03644	2 ^[x]
13.	D. S. Krotov, A. A. Valyuzhenich, “On degree-$3$ and $(n-4)$-correlation-immune perfect colorings of $n$-cubes”, Discrete Mathematics, 347:10 (2024), 114138 , 14 pp.
14.	D. S. Krotov, “On the existence of some completely regular codes in Hamming graphs”, ISIT 2024 (Athens, Greece, 7–12 July 2024), IEEE International Symposium on Information Theory – Proceedings, IEEE, 2024, 121–126

2023
15.	M. Shi, Y. Li, W. Cheng, D. Crnković, D. Krotov, P. Solé, “Self-dual bent sequences for complex Hadamard matrices”, Designs, Codes and Cryptography, 91:4 (2023), 1453–1474 https://rdcu.be/c1DT3	2 ^[x]
16.	M. Shi, Y. Li, W. Cheng, D. Crnković, D. Krotov, P. Solé, “Self-dual Hadamard bent sequences”, Journal of Systems Science and Complexity, 36:2 (2023), 894–908 https://rdcu.be/dai1l, arXiv: 2203.16439	1 ^[x]
17.	M. Shi, D. S. Krotov, “An enumeration of 1-perfect ternary codes”, Discrete Mathematics, 346:7 (2023), 113437 , 16 pp., arXiv: 2110.06305	4 ^[x]
18.	D. S. Krotov, “Perfect colorings of the infinite square grid: coverings and twin colors”, The Electronic Journal of Combinatorics, 30:2 (2023), #P2.4 , 59 pp., arXiv: 2010.15839	1 ^[x]
19.	M. Shi, X. Li, D. S. Krotov, F. Özbudak, “Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings”, IEEE Transactions on Information Theory, 69:9 (2023), 5597–5603 , arXiv: 2305.02735	1 ^[x]
20.	D. S. Krotov, “Projective tilings and full-rank perfect codes”, Designs, Codes and Cryptography, 91:10 (2023), 3293–3303 https://rdcu.be/desVK, arXiv: 2207.00105
21.	M. Shi, Y. Xia, D. S. Krotov, “A family of diameter perfect constant-weight codes from Steiner systems”, Journal of Combinatorial Theory, Series A, 200 (2023), 105790 , 20 pp., arXiv: 2212.00048	4 ^[x]

2022
22.	M. Shi, D. Krotov, P. Solé, “On the coset graph construction of distance-regular graphs”, Discrete Mathematics, 345:11 (2022), 113037 , 6 pp., arXiv: 2206.00031	1 ^[x]
23.	M. Shi, R. Wu, D. S. Krotov, “On $q$-ary shortened-$1$-perfect-like codes”, IEEE Transactions on Information Theory, 68:11 (2022), 7100–7106 , arXiv: 2110.05256	2 ^[x]

2021
24.	D. S. Krotov, V. N. Potapov, “On multifold packings of radius-1 balls in Hamming graphs”, IEEE Transactions on Information Theory, 67, "From Deletion-Correction to Graph Reconstruction: In Memory of Vladimir I. Levenshtein:6 (2021), 3585–3598 , arXiv: 1902.00023	6 ^[x]
25.	E. A. Bespalov, D. S. Krotov, A. A. Matiushev, A. A. Taranenko, K. V. Vorobev, “Perfect 2‐colorings of Hamming graphs”, Journal of Combinatorial Designs, 29:6 (2021), 367-396 https://onlinelibrary.wiley.com/share/author/UYZBZKEKTQJVVPN66YAW?target=10.1002/jcd.21771, arXiv: 1911.13151	10 ^[x]
26.	M. J. Shi, S. K. Wang, X. X. Li, D. S. Krotov, “On the number of frequency hypercubes $F^n(4;2,2)$”, Siberian Mathematical Journal, 62:5 (2021), 951–962 https://rdcu.be/cylBU, arXiv: 2005.10887

2020
27.	Y. Guan, M. J. Shi, D. S. Krotov, “Steiner triple systems of order 21 with a transversal subdesign TD(3,6)”, Problems of Information Transmission, 56:1 (2020), 23–32 https://rdcu.be/b3Ccw, arXiv: 1905.09081
28.	D. S. Krotov, “The existence of perfect codes in Doob graphs”, IEEE Transactions on Information Theory, 66:3 (2020), 1423–1427 , arXiv: 1810.03772	4 ^[x]
29.	M. Shi, D. Krotov, P. Solé, “A new approach to the Kasami codes of type 2”, IEEE Transactions on Information Theory, 66:4 (2020), 2456–2465 , arXiv: 1810.00015	5 ^[x]
30.	M. Shi, L. Xu, D. S. Krotov, “On the number of resolvable Steiner triple systems of small 3-rank”, Designs, Codes and Cryptography, 88:6 (2020), 1037–1046 https://rdcu.be/b1dkk, arXiv: 1907.00266	1 ^[x]
31.	D. S. Krotov, “On the OA(1536,13,2,7) and related orthogonal arrays”, Discrete Mathematics, 343:2 (2020), 111659 , 11 pp., arXiv: 1905.11371	8 ^[x]
32.	E. Ghorbani, S. Kamali, G. B. Khosrovshahi, D. S. Krotov, “On the volumes and affine types of trades”, The Electronic Journal of Combinatorics, 27:1 (2020), #P1.29 , 28 pp., arXiv: 1810.02296	1 ^[x]
33.	D. S. Krotov, K. V. Vorobev, “On unbalanced Boolean functions with best correlation immunity”, The Electronic Journal of Combinatorics, 27:1 (2020), #P1.45 , 24 pp., arXiv: 1812.02166	3 ^[x]

2019
34.	M. Shi, D. Huang, D. Krotov, “Additive perfect codes in Doob graphs”, Designs, Codes and Cryptography, 87:8 (2019), 1857–1869 https://rdcu.be/bcaQW, arXiv: 1806.04834	10 ^[x]
35.	M. Shi, R. Wu, D. S. Krotov, “On $Z_pZ_{p^k}$-additive codes and their duality”, IEEE Transactions on Information Theory, 65:6 (2019), 3841–3847 , arXiv: 1809.00008	46 ^[x]
36.	M. Shi, D. S. Krotov, P. Solé, “A new distance-regular graph of diameter 3 on 1024 vertices”, Designs, Codes and Cryptography, 87:9 (2019), 2091–2101 https://rdcu.be/biitT, arXiv: 1806.07069	9 ^[x]
37.	E. V. Gorkunov, D. S. Krotov, V. N. Potapov, “On the number of autotopies of an $n$-ary qusigroup of order $4$”, Quasigroups and Related Systems, 27:2 (2019), 227–250 http://www.quasigroups.eu/contents/download/2019/27_22.pdf, arXiv: 1903.00188
38.	M. Shi, L. Xu, D. S. Krotov, “The number of the non-full-rank Steiner triple systems”, Journal of Combinatorial Designs, 27:10 (2019), 571–585 , arXiv: 1806.00009	5 ^[x]
39.	D. S. Krotov, “On (2n/3−1)-resilient (n,2)-functions”, ISIT 2019 (Paris, France, 7–12 July 2019), IEEE International Symposium on Information Theory - Proceedings, IEEE, 2019, 2957–2961 https://arXiv.org/abs/1902.00022
40.	D. S. Krotov, “On dual codes in the Doob schemes”, ISIT 2019 (Paris, France, 7–12 July 2019), IEEE International Symposium on Information Theory - Proceedings, IEEE, 2019, 1917–1921 https://arxiv.org/abs/1902.00020	2 ^[x]
41.	D. S. Krotov, V. N. Potapov, “On two-fold packings of radius-1 balls in Hamming graphs”, ISIT 2019 (Paris, France, 7–12 July 2019), IEEE International Symposium on Information Theory - Proceedings, IEEE, 2019, 2773–2777	1 ^[x]
42.	D. S. Krotov, V. N. Potapov, “On the cardinality spectrum and the number of latin bitrades of order 3”, Problems of Information Transmission, 55:4 (2019), 343–365 https://rdcu.be/b0Kty

2018
43.	D. S. Krotov, “On the gaps of the spectrum of volumes of trades”, Journal of Combinatorial Designs, 26:3 (2018), 119–126	3 ^[x]
44.	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 https://rdcu.be/29aE, arXiv: 1510.01429
45.	D. S. Krotov, I. Yu. Mogilnykh, A. Yu. Vasileva, On completely regular codes of covering radius 1 in the halved hypercubes, 2018 (Published online) , 8 pp., arXiv: 1812.03159

2017
46.	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 https://rdcu.be/6gCz, arXiv: 1602.00036
47.	E. A. Bespalov, D. S. Krotov, “MDS codes in Doob graphs”, Problems of Information Transmission, 53:2 (2017), 136–154 https://rdcu.be/dJ8v4
48.	D. S. Krotov, “The extended 1-perfect trades in small hypercubes”, Discrete Mathematics, 340:10 (2017), 2559–2572 , arXiv: 1512.03421	8 ^[x]
49.	D. S. Krotov, “The minimum volume of subspace trades”, Discrete Mathematics, 340:12 (2017), 2723–2731 , arXiv: 1512.02592	4 ^[x]

2016
50.	D. S. Krotov, “Perfect Codes in Doob Graphs”, Designs, Codes and Cryptography, 80:1 (2016), 91–102 https://rdcu.be/6gzd, arXiv: 1407.6329	9 ^[x]
51.	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	2 ^[x]
52.	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	24 ^[x]
53.	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 https://rdcu.be/dJ8v7
54.	D. S. Krotov, V. N. Potapov, “Constructions of Transitive Latin Hypercubes”, European Journal of Combinatorics, 54 (2016), 51–64 , arXiv: 1303.0004	1 ^[x]
55.	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	4 ^[x]
56.	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 https://rdcu.be/dJ8v6, arXiv: 1512.03048
57.	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

2015
58.	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	21 ^[x]
59.	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	4 ^[x]
60.	D. S. Krotov, “On the Number of Maximum Independent Sets in Doob Graphs”, Siberian Electronic Mathematical Reports, 12 (2015), 508–512 , arXiv: 1612.00007	1 ^[x]
61.	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	31 ^[x]

2014
62.	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	1 ^[x]
63.	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	4 ^[x]
64.	D. S. Krotov, “On Calculation of the Interweight Distribution of an Equitable Partition”, Journal of Algebraic Combinatorics, 40:2 (2014), 373–386 https://rdcu.be/dJ8wb, arXiv: 1303.0002	4 ^[x]

2015
65.	K. V. Vorobev, 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 https://rdcu.be/dJ8v9

2013
66.	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	2 ^[x]

2012
67.	D. S. Krotov, “On the Binary Codes with Parameters of Triply-Shortened 1-Perfect Codes”, Designs, Codes and Cryptography, 64:3 (2012), 275–283 https://rdcu.be/dJ8wd, arXiv: 1104.0005	8 ^[x]

2011
68.	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
69.	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	5 ^[x]
70.	D. S. Krotov, “On Weight Distributions of Perfect Colorings and Completely Regular Codes”, Designs, Codes and Cryptography, 61:3 (2011), 315–329 https://rdcu.be/dJ8wf, arXiv: 0907.0001	20 ^[x]
71.	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	11 ^[x]
72.	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	9 ^[x]

2010
73.	D. S. Krotov, “On the Binary Codes with Parameters of Doubly-Shortened $1$-Perfect Codes”, Designs, Codes and Cryptography, 57:2 (2010), 181–194 https://rdcu.be/dJ8wi, arXiv: 0907.0002	13 ^[x]

2011
74.	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 https://rdcu.be/dJ8wh, arXiv: 1104.0003

2010
75.	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 https://rdcu.be/dJ8wg

2009
76.	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	25 ^[x]
77.	S. V. Avgustinovich, D. S. Krotov, “Embedding in a Perfect Code”, Journal of Combinatorial Designs, 17:5 (2009), 419–423 , arXiv: 0804.0006	8 ^[x]

2008
78.	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	9 ^[x]
79.	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
80.	D. S. Krotov, “On Diameter Perfect Constant-Weight Ternary Codes”, Discrete Mathematics, 308:14 (2008), 3104–3114 , arXiv: math/0509620	5 ^[x]
81.	D. S. Krotov, “On Reducibility of $n$-Ary Quasigroups”, Discrete Mathematics, 308:22 (2008), 5289–5297 , arXiv: math/0607284	8 ^[x]
82.	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	8 ^[x]
83.	D. S. Krotov, “On Irreducible $n$-Ary Quasigroups with Reducible Retracts”, European Journal of Combinatorics, 29:2 (2008), 507–513 , arXiv: math/0607785	7 ^[x]
84.	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	9 ^[x]
85.	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)

2009
86.	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

2007
87.	D. S. Krotov, “$Z_{2^k}$-Dual Binary Codes”, IEEE Transactions on Information Theory, 53:4 (2007), 1532–1537 , arXiv: math/0509325	35 ^[x]

2006
88.	V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order 4”, Siberian Mathematical Journal, 47:4 (2006), 720–731 https://rdcu.be/dJ8wk, arXiv: math/0605104

2004
89.	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 https://rdcu.be/dJ8wl

2001
90.	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	54 ^[x]
91.	D. S. Krotov, “Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3”, Problems of Information Transmission, 37:1 (2001), 1–9 https://rdcu.be/dJ8wm

2000
92.	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)
93.	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
94.	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
95.	D. S. Krotov, “Combining Construction of Perfect Binary Codes”, Problems of Information Transmission, 36:4 (2000), 349–353

Presentations in Math-Net.Ru

1.	On the eigenvectors of the quotient matrix of a perfect coloring of a Q-polynomial graph. D. S. Krotov, V. N. Potapov 2024-ary quasigroups and related topics May 24, 2024 11:00
2.	On the classification of perfect colorings of small degree in the hypercube D. S. Krotov 2024-ary quasigroups and related topics June 23, 2023
3.	Projective tilings and full-rank perfect codes D. S. Krotov 2024-ary quasigroups and related topics September 17, 2021 11:00
4.	Совершенные коды и их обобщения: проблема существования D. S. Krotov August 9, 2021 11:10
5.	Bipartite perfect colorings of the infinite square grid: twin colors and the covering case D. S. Krotov 2024-ary quasigroups and related topics October 30, 2020 11:00
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