Persons: Potapov, Vladimir Nikolaevich

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Potapov, Vladimir Nikolaevich

Statistics
in MathSciNet:	60 (60)
in zbMATH:	55 (55)
in Web of Science:	55 (55)
in Scopus:	63 (63)

Candidate of physico-mathematical sciences (1997)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

E-mail:

Website:

https://math.nsc.ru/~potapov

Keywords:

Boolean functions; matchings; Hamiltonian cycles; Latin squares; $n$-ary quasigroups; error-correcting codes; bent functions, combinatorial designs, perfect coloring, source coding; data retrieval; hash-functions; combinatorics on words; video coding, genetic sequences; entropy and widths; wavelets.

Subject:

information theory, cryptography, coding theory, combinatorics

Main publications:

V. N. Potapov, “On the number of SQSs, latin hypercubes and MDS codes”, Journal of Combinatorial Designs, 26:5 (2018), 237–248
D. S. Krotov, V. N. Potapov, “Propelinear 1-perfect codes from quadratic functions”, IEEE Trans. Inform. Theory, 60:4 (2014), 2065–2068
V. N. Potapov, Vvedenie v teoriyu informatsii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2014 , 152 pp.
V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Siberian Math. J., 52:2 (2011), 303–310
D. S. Krotov, V. N. Potapov, “n-Ary quasigroups of order 4”, SIAM J. Discrete Math., 23:2 (2009), 561–570

https://www.mathnet.ru/eng/person18014

https://scholar.google.com/citations?user=0DynDV0AAAAJ&hl=en

https://zbmath.org/authors/ai:potapov.vladimir-n

https://mathscinet.ams.org/mathscinet/MRAuthorID/342859

https://elibrary.ru/author_items.asp?authorid=15017

https://orcid.org/0000-0001-9461-2064

https://www.webofscience.com/wos/author/record/A-1997-2011

https://www.scopus.com/authid/detail.url?authorId=7102561165

https://www.researchgate.net/profile/Vladimir_Potapov2

https://arxiv.org/a/Potapov_V_1

List of publications:

scientific publications

by years

by types

by times cited

common list

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

1.	Y. L. Orlov, V. N. Potapov, “Complexity: an internet resource for analysis of DNA sequence complexity”, Nucl. Acids. Res., 32 (2004), 628–633	73 ^[x]
2.	V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order 4”, Siberian Math. J., 47:4 (2006), 720–731
3.	D. S. Krotov, I. Yu. Mogilnykh, V. N. Potapov, “To the theory of q-ary Steiner and other-type trades”, Discrete Math., 339:3 (2016), 1150–1157	25 ^[x]
4.	D. S. Krotov, V. N. Potapov, “n-Ary quasigroups of order 4”, SIAM J. Discrete Math., 23:2 (2009), 561–570	25 ^[x]
5.	V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Problems Inform. Transmission, 48:1 (2012), 47–55
6.	V. N. Potapov, D. S. Krotov, “On the number of n-ary quasigroups of finite order”, Discrete Math. Appl., 21:5-6 (2011), 575–585
7.	V. N. Potapov, “Multidimensional Latin bitrades”, Siberian Math. J., 54:2 (2013), 317–324
8.	V. N. Potapov, “On perfect 2-colorings of the q-ary n-cube”, Discrete Math., 312:6 (2012), 1269–1272	12 ^[x]
9.	D. S. Krotov, V. N. Potapov, “On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes”, Problems Inform. Transmission, 40:1 (2004), 5–12
10.	V. N. Potapov, “On extensions of partial $n$-quasigroups of order 4”, Siberian Adv. Math., 22:2 (2012), 135–151
11.	V. N. Potapov, “A lower bound for the number of transitive perfect codes”, J. Appl. Industr. Math., 1:3 (2007), 373–379
12.	V. N. Potapov, “On perfect colorings of Boolean $n$-cube and correlation immune functions with small density”, Sib. Èlektron. Mat. Izv., 7 (2010), 372–382
13.	A. Greshnov, V. Potapov, “About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics”, AIMS Mathematics, 8:3 (2023), 6191–6205	7 ^[x]
14.	V. N. Potapov, “Constructions of pairs of orthogonal latin cubes”, Journal of Combinatorial Designs, 28:8 (2020), 604–613 , arXiv: 1911.12960	7 ^[x]
15.	V. N. Potapov, A. A. Taranenko, Yu. V. Tarannikov, “An asymptotic lower bound on the number of bent functions”, Designs, Codes and Cryptography, 92:3, Special Issue: Coding and Cryptography 2022 (2024), 639–651 , arXiv: 2108.00232	6 ^[x]
16.	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]
17.	S. Kitaev , V. N. Potapov, V. Vajnovszki, “On shortening u-cycles and u-words for permutations”, Discrete Appl. Math., 260 (2019), 203–213 , arXiv: math.CO/1707.06110	6 ^[x]
18.	V. N. Potapov, “On Minimal Distance Between q-ary Bent Functions”, 2016 XV International Symposium "Problems of Redundancy in Information and Control Systems (Saint-Petersburg, 26-29 September 2016), IEEE, 2016, 115–116	6 ^[x]
19.	V. N. Potapov, “Redundancy estimates for the Lempel–Ziv algorithm of data compression”, perevod: Otsenki izbytochnosti kodirovaniya posledovatelnostei algoritmom Lempela–Ziva, Discrete Appl. Math., 135:1-3 (2004), 245–254	6 ^[x]
20.	A. L. Perezhogin, V. N. Potapov, “On the number of Hamiltonian cycles in a Boolean cube”, Diskretn. Anal. Issled. Oper., 8:2 (2001), 52–62
21.	V. N. Potapov, S. V. Avgustinovich, Siberian Math. J., 61:5 (2020), 867–877
22.	V. N. Potapov, “On the number of SQSs, latin hypercubes and MDS codes”, Journal of Combinatorial Designs, 26:5 (2018), 237–248	5 ^[x]
23.	D. S. Krotov, V. N. Potapov, “On connection between reducibility of an n-ary quasigroup and that of its retracts”, Discrete Math., 311:1 (2011), 58–66	5 ^[x]
24.	V. N. Potapov, “A survey of methods for the undistorted coding of discrete sources”, Diskretn. Anal. Issled. Oper., 6:4 (1999), 49–91
25.	D. S. Krotov, V. N. Potapov, “Propelinear 1-perfect codes from quadratic functions”, IEEE Trans. Inform. Theory, 60:4 (2014), 2065–2068	4 ^[x]
26.	V. N. Potapov, “Infinite-Dimensional Quasigroups of Finite Orders”, Math. Notes, 93:3 (2013), 479–486
27.	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
28.	S. Avgustinovich, S. Kitaev, J. Liese, V. Potapov, A. Taranenko, “Singleton mesh patterns in multidimensional permutations”, J. Combin. Theory, Ser. A, 201 (2024), 105801 , 23 pp., arXiv: 2208.12845	3 ^[x]
29.	V. N. Potapov, “An Upper Bound on the Number of Bent Functions”, Proceedings of 2021 XVII International Symposium on Problems of Redundancy in Information and Control Systems (Moskva, 25–29 oktyabrya 2021 g.), IEEE, 2021, 95–96	3 ^[x]
30.	V. N. Potapov, “On q-ary bent and plateaued functions”, Des. Codes Cryptography, 88:10 (2020), 2037–2049 , arXiv: 1911.06973	3 ^[x]
31.	D. S. Krotov, V. N. Potapov, “On the cardinality spectrum and the number of latin bitrades of order $3$”, Problems Inform. Transmission, 55:4 (2019), 343–365
32.	V. N. Potapov, “Lower bound on the number of Boolean functions with median correlation immunity”, 2019 XVI International Symposium “Problems of Redundancy in Information and Control Systems” (21-25 October 2019, Moscow, Russia), IEEE, 2019, 45–46	3 ^[x]
33.	V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. Èlektron. Mat. Izv., 11 (2014), 451–456
34.	A. Filippov, V. Rufitskiy, V. Potapov, “Scalar-quantization-based multi-layer data hiding for video coding applications”, Visual Communications and Image Processing Conference, IEEE, 2014, 262–265	3 ^[x]
35.	S. Avgustinovich , S. Kitaev, V. N. Potapov, V. Vajnovszki, “Gray coding cubic planar maps”, Theoret. Comput. Sci., 616 (2016), 59–69	2 ^[x]
36.	V. N. Potapov, “On the number of transversals in latin squares”, Discrete Appl. Math., 202 (2016), 194–196	2 ^[x]
37.	V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Siberian Math. J., 52:2 (2011), 303–310
38.	N. Alon, J. Balogh, V. N. Potapov, “Partitioning the hypercube into smaller hypercubes”, Illinois J. Math., 69:1 (2025), 109–122 , arXiv: 2401.00299	1 ^[x]
39.	V. N. Potapov, F. Ozbudak, “Asymptotic bounds on the numbers of certain bent functions”, Cryptography and Communications, 16:6, Boolean Fuctions and Their Applications VIII 2023 (2024), 1289 - 1307	1 ^[x]
40.	A. L. Perezhogin, V. N. Potapov, S. Yu. Vladimirov, “Every latin hypercube of order 5 has transversals”, Journal of Combinatorial designs, 32:11 (2024), 679–699 , arXiv: 2311.14997	1 ^[x]
41.	V. N. Potapov, “Existence of balanced functions that are not derivative of bent functions”, 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (24-27 October 2023 Moscow, Russia), IEEE, 2023 https://arxiv.org/abs/2309.04244	1 ^[x]
42.	V. N. Potapov, “Embedding in MDS codes and Latin cubes”, Journal of Combinatorial Designs, 30:9 (2022), 626–633 , arXiv: 2109.14962	1 ^[x]
43.	V. N. Potapov, “DP-colorings of uniform hypergraphs and splittings of Boolean hypercube into faces”, Electronic Journal of Combinatorics, 29:3 (2022), 3.37 , 7 pp., arXiv: 1905.04461	1 ^[x]
44.	D. S. Krotov , V. N. Potapov, “On two-fold packings of radius-1 balls in Hamming graphs”, 2019 IEEE International Symposium on Information Theory (7–12 July 2019 Paris, France), IEEE, 2019, 2773–2777	1 ^[x]
45.	D. S. Krotov, V. N. Potapov, “Constructions of transitive latin hypercubes”, European Journal of Combinatorics, 54:1 (2016), 51–64	1 ^[x]
46.	V. N. Potapov, “Construction of Hamiltonian cycles with a given range of directions of edges in the Boolean $n$-dimensional cube”, J. Appl. Industr. Math., 6:3 (2012), 339–345
47.	V. N. Potapov, “On almost balanced Boolean functions”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 23–25
48.	V. N. Potapov, “Arithmetic coding of messages using random sequence”, Prikl. Diskr. Mat., 2008, no. 2(2), 131–133
49.	V. N. Potapov, “On the maximum length of binary words with bounded frequency of units and without identical subwords of given length”, Diskretn. Anal. Issled. Oper., 11:3 (2004), 48–58
50.	V. N. Potapov, “Additive complexity of words with restrictions on the composition of subwords”, Diskretn. Anal. Issled. Oper., 11:1 (2004), 52–78
51.	R. E. Krichevskii, V. N. Potapov, “Rapid encoding of run lengths and pyramid cubic lattices”, IEEE Trans. Inform. Theory, 45:4 (1999), 1347–1350	1 ^[x]
52.	V .N. Potapov, A. A. Taranenko, “Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices”, Discrete Mathematics, 349:1 (2026), 114653 , arXiv: 2406.14160
53.	D. S. Krotov, V. N. Potapov, Completely Regular Codes in Distance-Regular Graphs, v. 1, Monographs and Research Notes in Mathematics, Completely regular codes and equitable partitions, eds. Shi, M., Sole, P., Chapman & Hall/CRC, 2025 , 83 pp.
54.	A.L. Perezhogin, V.N. Potapov, A.A. Taranenko, S.Y. Vladimirov, “Characterization of polystochastic matrices of order 4 with zero permanent”, Journal of Combinatorial Theory. Series A., 2015, 106060 (2025), 1–23 , arXiv: 2410.09546
55.	V. N. Potapov, “On the number of relevant variables for discrete functions”, Cryptography and Communications, 17, Boolean Functions and Their Applications, 2024 (2025), 1–10 , arXiv: 2410.21937
56.	D. S. Krotov,, F. Özbudak, V. N. Potapov, “Generalizing the Bierbrauer–Friedman bound for orthogonal arrays”, Des. Codes Cryptogr., 2025 , arXiv: 2411.16559
57.	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
58.	V. N. Potapov, “Upper bounds on the numbers of binary plateaued and bent functions”, Cryptography and Comm., 16:6, Boolean Functions and their Applications VIII (2024), 1347 - 1356 , arXiv: 2303.16547
59.	V. N. Potapov, “Shaping algorithm for high order QAM”, Matematicheskii forum (Itogi nauki, Yug Rossii) (Vladikavkaz 29 iyunya - 5 iyulya), ISSN: 2225-4242, 15, 2023, 124-125
60.	V. N. Potapov, On extremal properties of perfect 2-colorings, 2022 (Published online) , 9 pp., arXiv: 2204.03308
61.	V. N. Potapov, “On Weight Spectrum of Linear Codes”, Proceedings of 2021 XVII International Symposium on Problems of Redundancy in Information and Control Systems (Moskva, 25–29 oktyabrya 2021 g.), IEEE, 2021, 116–118
62.	V. N. Potapov, “Ob universalnykh po Voronenko funktsiyakh”, Vestnik Moskovskogo Universiteta. Ser. 15, 2021 (to appear) text
63.	E. V. Gorkunov, D. S. Krotov, V. N. Potapov, “On the number of autotopies of an n-ary quasigroup of order 4”, Quasigroups and Related Systems, 27:2 (2019), 227–259 http://www.quasigroups.eu/contents/download/2019/27_22.pdf
64.	V. N. Potapov, “On minimal distance between q-ary plateaued functions”, 2019 XVI International Symposium “Problems of Redundancy in Information and Control Systems” (21-25 October 2019, Moscow, Russia), IEEE, 2019, 42–44
65.	Vladimir N. Potapov, “Partial covering arrays for data hiding and quantization”, Sib. elektron. matem. izv., 15 (2018), 561–569
66.	V. N. Potapov, “Linear Codes for an Effective Quantization of Data”, 2016 XV International Symposium "Problems of Redundancy in Information and Control Systems (Saint-Petersburg, 26-29 September 2016), IEEE, 2016, 116–117
67.	V. N. Potapov, “Properties of $p$-ary bent functions that are at minimal distance from each other”, Prikl. Diskr. Mat. Suppl., 2015, no. 8, 39–43
68.	V. N. Potapov, Vvedenie v teoriyu informatsii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2014 , 152 pp.
69.	V. Potapov, N. Shlyakhov, A. Silantiev, M. Tchobanou, “What could be after HEVC?”, Proceedings of 9th International Conference, Information, Communications and Signal Processing (ICICS), 2013, 1–5
70.	V. N. Potapov, “On perfect 2-colorings of the $q$-ary hypercube”, Prikl. Diskr. Mat., 2011, no. supplement № 4, 18–20
71.	A. V. Greshnov, S. A. Malyugin, V. N, Potapov, Sbornik zadach i uprazhnenii po matematicheskomu analizu. 2-i semestr, Novosib. gos. un-t., Novosibirsk, 2009 , 240 pp.
72.	D. S. Krotov, V. N. Potapov, P. V. Sokolova, “On reconstructing reducible n-ary quasigroups and switching subquasigroups”, Quasigroups and Related Systems, 16 (2008), 55–67
73.	A. V. Greshnov, S. A. Malyugin , V. N. Potapov, Sbornik zadach i uprazhnenii po matematicheskomu analizu. 1-i semestr, Novosib. gos. un-t., Novosibirsk, 2008 , 150 pp.
74.	D. C. Krotov, V. N. Potapov, “Konstruktsii n-kvazigrupp”, Vestnik TGU. Prilozhenie, 23 (2007), 35–36
75.	Yu. L. Orlov, Potapov, V. N. Potapov, A. S. Poplavsky, “Computer analysis of genomic sequence complexity: New applications”, Proceedings of the Fourth International Conference on Bioinformatics of Genome Regulation and Structure, Vol 1 (Novosibirsk, July 25-30, 2004), 2004, 153-157
76.	Y. L. Orlov, V. D. Gusev, L. A. Nemytikova, V. N. Potapov, N. A. Kolchanov, “Internet-available software packages for analysis of DNA sequence complexity”, Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'03 (Las Vegas, NV, June 23-26, 2003), eds. Valafar, F, 2003, 35-38
77.	Y. L. Orlov, V. P. Filippov, V. N. Potapov , N. A. Kolchanov, “Construction of stochastic context trees for genetic texts”, In Silico Biology, 2:3 (2002), 233–247
78.	V. N. Potapov, “Numeratsiya tselochislennogo simpleksa”, Vestnik NNGU. Matematicheskoe modelirovanie i optimalnoe upravlenie, 22:1 (2000), 152–158
79.	Yu. L. Orlov, V. N. Potapov, “Otsenka stokhasticheskoi slozhnosti geneticheskikh tekstov”, Vychislitelnye tekhnologii, 5, spetsvypusk (2000), 5–15 annotation
80.	V. N. Potapov, “Estimates for the redundancy of the coding of sequences by the Lempel–Ziv algorithm”, Diskretn. Anal. Issled. Oper., 6:2 (1999), 70–81
81.	V. N. Potapov, Teoriya informatsii. Kodirovanie diskretnykh veroyatnostnykh istochnikov, Izd. tsentr NGU, 1999 , 71 pp.
82.	V. N. Potapov, “$\varepsilon$-entropy of compacta in $C$, and tabulation of continuous functions”, Siberian Math. J., 38:4 (1997), 759–771
83.	R. E. Krichevskii, V. N. Potapov, “Enumeration of rare events, pyramid and ball cubic lattices”, Proceedings of 1997 IEEE International Symposium on Information Theory, IEEE, 1997, 19
84.	R. E. Krichevskii, V. N. Potapov, “Compression and restoration of square integrable function”, Electron. Res. Announc. Amer. Math. Soc., 2:1 (1996), 42–49
85.	V. N. Potapov, “Tabulirovanie gladkikh funktsii”, Mezhvuz. sb. nauch. tr. Analiz i diskretnaya matematika, NGU, Novosibirsk, 1995, 115–125
86.	R. E. Krichevskii, V. N. Potapov, “Compression of square integrable function: Fourier vs wavelets”, Proceedings of 1995 IEEE International Symposium on Information Theory, IEEE, 1995, 431
87.	R. E. Krichevskii, V. N. Potapov, “Combinatorial Source Encoding and Perfect Hashing”, Proceedings of 1994 IEEE International Symposium on Information Theory, IEEE, 1994, 319
88.	V. N. Potapov, “Fast lexicographic search”, Dokl. Math., 47:3 (1993), 431–434

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.	Every latin hypercube of order 5 contains transversals A. L. Perezhogin, V. N. Potapov, S. Yu. Vladimirov 2024-ary quasigroups and related topics September 15, 2023 11:00
3.	Embedding in MDS codes and Latin cubes V. N. Potapov 2024-ary quasigroups and related topics September 24, 2021 11:00
4.	On the XVI International Symposium “Problems of Redundancy in Information and Control Systems” V. N. Potapov 2024-ary quasigroups and related topics November 1, 2019
5.	Perfect Coloring of Hypercube and Discrete Fourier Transforms V. N. Potapov Seminar on Coding Theory November 12, 2013 19:00
6.	Information theory and encoding. Lecture 4 V. N. Potapov Summer School "Contemporary Mathematics", 2012 July 29, 2012 15:30
7.	Information theory and encoding. Lecture 3 V. N. Potapov Summer School "Contemporary Mathematics", 2012 July 28, 2012 11:15
8.	Information theory and encoding. Lecture 2 V. N. Potapov Summer School "Contemporary Mathematics", 2012 July 24, 2012 17:00
9.	Information theory and encoding. Lecture 1 V. N. Potapov Summer School "Contemporary Mathematics", 2012 July 23, 2012 09:30

Organisations