Persons: Potapov, Vladimir Nikolaevich

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Potapov, Vladimir Nikolaevich

Total publications:	83 (83)
in MathSciNet:	52 (52)
in zbMATH:	47 (47)
in Web of Science:	43 (43)
in Scopus:	53 (53)
Cited articles:	47
Citations:	331
Presentations:	9

Number of views:
This page:	9729
Abstract pages:	9659
Full texts:	3074
References:	872

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 cube; matching; Hamiltonian cycles; Latin squares; $n$-quasigroups; perfect codes; perfect coloring, source coding; data retrieval; hash-functions; combinatorics on words; genetic sequences; entropy and widths; wavelets.

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

List of publications on ZentralBlatt

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

Full list of publications:

scientific publications

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


2024
1.	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
2.	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	1 ^[x]
3.	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	3 ^[x]
4.	V. N. Potapov, F. Ozbudak, “Asymptotic bounds on the numbers of certain bent functions”, Cryptography and Communications, 2024, Boolean Functions and Their Applications VIII 2023
5.	D. S.Krotov, V. N. Potapov, Completely Regular Codes and Equitable Partitions, text, 2024 (to appear)
6.	N. Alon, J. Balogh, V. N. Potapov, Partitioning the hypercube into smaller hypercubes, 2024 (Published online) , arXiv: 2401.00299
7.	V. N. Potapov, A. A. Taranenko, Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices, 2024 (Published online) , arXiv: 2406.14160 [math.CO]
8.	A. L. Perezhogin, V. N. Potapov, S. Yu. Vladimirov, “Every latin hypercube of order 5 has transversals”, Journal of Combinatorial designs, 2024 , arXiv: 2311.14997

2023
9.	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	3 ^[x]
10.	V. N. Potapov, Upper bounds on the numbers of binary plateaued and bent functions, 2023 , arXiv: 2303.16547
11.	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
12.	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

2022
13.	V. N. Potapov, “Embedding in MDS codes and Latin cubes”, Journal of Combinatorial Designs, 30:9 (2022), 626–633 , arXiv: 2109.14962	1 ^[x]
14.	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]
15.	V. N. Potapov, On extremal properties of perfect 2-colorings, 2022 (Published online) , 9 pp., arXiv: 2204.03308

2021
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.	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
18.	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	2 ^[x]
19.	V. N. Potapov, “Ob universalnykh po Voronenko funktsiyakh”, Vestnik Moskovskogo Universiteta. Ser. 15, 2021 (to appear) text

2020
20.	V. N. Potapov, S. V. Avgustinovich, Siberian Math. J., 61:5 (2020), 867–877
21.	V. N. Potapov, “On q-ary bent and plateaued functions”, Des. Codes Cryptography, 88:10 (2020), 2037–2049 , arXiv: 1911.06973	2 ^[x]
22.	V. N. Potapov, “Constructions of pairs of orthogonal latin cubes”, Journal of Combinatorial Designs, 28:8 (2020), 604–613 , arXiv: 1911.12960	7 ^[x]

2019
23.	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
24.	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	4 ^[x]
25.	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
26.	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]
27.	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	2 ^[x]
28.	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

2018
29.	Vladimir N. Potapov, “Partial covering arrays for data hiding and quantization”, Sib. elektron. matem. izv., 15 (2018), 561–569
30.	V. N. Potapov, “On the number of SQSs, latin hypercubes and MDS codes”, Journal of Combinatorial Designs, 26:5 (2018), 237–248	4 ^[x]

2016
31.	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	22 ^[x]
32.	D. S. Krotov, V. N. Potapov, “Constructions of transitive latin hypercubes”, European Journal of Combinatorics, 54:1 (2016), 51–64	1 ^[x]
33.	S. Avgustinovich , S. Kitaev, V. N. Potapov, V. Vajnovszki, “Gray coding cubic planar maps”, Theoret. Comput. Sci., 616 (2016), 59–69	1 ^[x]
34.	V. N. Potapov, “On the number of transversals in latin squares”, Discrete Appl. Math., 202 (2016), 194–196	2 ^[x]
35.	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
36.	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]

2015
37.	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

2014
38.	V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. Èlektron. Mat. Izv., 11 (2014), 451–456
39.	D. S. Krotov, V. N. Potapov, “Propelinear 1-perfect codes from quadratic functions”, IEEE Trans. Inform. Theory, 60:4 (2014), 2065–2068	4 ^[x]
40.	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]
41.	V. N. Potapov, Vvedenie v teoriyu informatsii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2014 , 152 pp.

2013
42.	V. N. Potapov, “Infinite-Dimensional Quasigroups of Finite Orders”, Math. Notes, 93:3 (2013), 479–486
43.	V. N. Potapov, “Multidimensional Latin bitrades”, Siberian Math. J., 54:2 (2013), 317–324
44.	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

2012
45.	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

2011
46.	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

2012
47.	V. N. Potapov, “On almost balanced Boolean functions”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 23–25
48.	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
49.	V. N. Potapov, “On perfect 2-colorings of the q-ary n-cube”, Discrete Math., 312:6 (2012), 1269–1272	11 ^[x]
50.	V. N. Potapov, “On extensions of partial $n$-quasigroups of order 4”, Siberian Adv. Math., 22:2 (2012), 135–151

2011
51.	V. N. Potapov, “On perfect 2-colorings of the $q$-ary hypercube”, Prikl. Diskr. Mat., 2011, no. supplement № 4, 18–20
52.	V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Siberian Math. J., 52:2 (2011), 303–310
53.	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]

2010
54.	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
55.	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

2009
56.	D. S. Krotov, V. N. Potapov, “n-Ary quasigroups of order 4”, SIAM J. Discrete Math., 23:2 (2009), 561–570	24 ^[x]
57.	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.

2008
58.	V. N. Potapov, “Arithmetic coding of messages using random sequence”, Prikl. Diskr. Mat., 2008, no. 2(2), 131–133
59.	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
60.	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.

2007
61.	D. C. Krotov, V. N. Potapov, “Konstruktsii n-kvazigrupp”, Vestnik TGU. Prilozhenie, 23 (2007), 35–36
62.	V. N. Potapov, “A lower bound for the number of transitive perfect codes”, J. Appl. Industr. Math., 1:3 (2007), 373–379

2006
63.	V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order 4”, Siberian Math. J., 47:4 (2006), 720–731

2004
64.	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
65.	V. N. Potapov, “Additive complexity of words with restrictions on the composition of subwords”, Diskretn. Anal. Issled. Oper., 11:1 (2004), 52–78
66.	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
67.	Y. L. Orlov, V. N. Potapov, “Complexity: an internet resource for analysis of DNA sequence complexity”, Nucl. Acids. Res., 32 (2004), 628–633	70 ^[x]
68.	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]

2002
69.	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

2001
70.	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

2000
71.	V. N. Potapov, “Numeratsiya tselochislennogo simpleksa”, Vestnik NNGU. Matematicheskoe modelirovanie i optimalnoe upravlenie, 22:1 (2000), 152–158
72.	Yu. L. Orlov, V. N. Potapov, “Otsenka stokhasticheskoi slozhnosti geneticheskikh tekstov”, Vychislitelnye tekhnologii, 5, spetsvypusk (2000), 5–15

1999
73.	V. N. Potapov, “A survey of methods for the undistorted coding of discrete sources”, Diskretn. Anal. Issled. Oper., 6:4 (1999), 49–91
74.	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
75.	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]
76.	V. N. Potapov, Teoriya informatsii. Kodirovanie diskretnykh veroyatnostnykh istochnikov, Izd. tsentr NGU, 1999 , 71 pp.

1997
77.	V. N. Potapov, “$\varepsilon$-entropy of compacta in $C$, and tabulation of continuous functions”, Siberian Math. J., 38:4 (1997), 759–771
78.	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

1996
79.	R. E. Krichevskii, V. N. Potapov, “Compression and restoration of square integrable function”, Electron. Res. Announc. Amer. Math. Soc., 2:1 (1996), 42–49

1995
80.	V. N. Potapov, “Tabulirovanie gladkikh funktsii”, Mezhvuz. sb. nauch. tr. Analiz i diskretnaya matematika, NGU, Novosibirsk, 1995, 115–125
81.	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

1994
82.	R. E. Krichevskii, V. N. Potapov, “Combinatorial Source Encoding and Perfect Hashing”, Proceedings of 1994 IEEE International Symposium on Information Theory, IEEE, 1994, 319

1993
83.	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 2023-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 2023-ary quasigroups and related topics September 15, 2023 11:00
3.	Embedding in MDS codes and Latin cubes V. N. Potapov 2023-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 2023-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

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