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Potapov, Vladimir Nikolaevich

Total publications: 85 (85)
in MathSciNet: 53 (53)
in zbMATH: 47 (47)
in Web of Science: 43 (43)
in Scopus: 55 (55)
Cited articles: 47
Citations: 333
Presentations: 9

Number of views:
This page:9864
Abstract pages:9991
Full texts:3253
References:1001
Potapov, Vladimir Nikolaevich
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:
  1. V. N. Potapov, “On the number of SQSs, latin hypercubes and MDS codes”, Journal of Combinatorial Designs, 26:5 (2018), 237–248  crossref  mathscinet  zmath  isi  scopus
  2. D. S. Krotov, V. N. Potapov, “Propelinear 1-perfect codes from quadratic functions”, IEEE Trans. Inform. Theory, 60:4 (2014), 2065–2068  crossref  mathscinet  zmath  isi  elib  scopus
  3. V. N. Potapov, Vvedenie v teoriyu informatsii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2014 , 152 pp.
  4. V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Siberian Math. J., 52:2 (2011), 303–310  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
  5. D. S. Krotov, V. N. Potapov, “n-Ary quasigroups of order 4”, SIAM J. Discrete Math., 23:2 (2009), 561–570  crossref  mathscinet  zmath  isi  elib  scopus

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 | by years | by types | by times cited | common list |


Citations (Crossref Cited-By Service + Math-Net.Ru)
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  crossref  mathscinet  zmath  isi  scopus
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  crossref  mathscinet  zmath  isi  scopus 1
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  crossref  mathscinet  zmath  isi  scopus 3
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  crossref  scopus
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, 32:11 (2024), 679–699 , arXiv: 2311.14997  crossref  mathscinet  scopus
9. V. N. Potapov, On the number of relevant variables for discrete functions, 2024 (Published online) , 10 pp., arXiv: 2410.21937
10. A. L. Perezhogin, V. N. Potapov, A. A. Taranenko, S. Yu. Vladimirov, Characterization of polystochastic matrices of order 4 with zero permanent, 2024 (Published online) , 17 pp., arXiv: 2410.09546
11. 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  crossref  mathscinet  isi  scopus 4
12. V. N. Potapov, Upper bounds on the numbers of binary plateaued and bent functions, 2023 , arXiv: 2303.16547
13. 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  crossref  scopus
14. 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  elib
15. V. N. Potapov, “Embedding in MDS codes and Latin cubes”, Journal of Combinatorial Designs, 30:9 (2022), 626–633 , arXiv: 2109.14962  crossref  mathscinet  isi  scopus 1
16. 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  crossref  mathscinet  zmath  isi  scopus 1
17. V. N. Potapov, On extremal properties of perfect 2-colorings, 2022 (Published online) , 9 pp., arXiv: 2204.03308
18. 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  crossref  mathscinet  zmath  isi  scopus 6
19. 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  crossref  scopus
20. 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  crossref  scopus 2
21. V. N. Potapov, “Ob universalnykh po Voronenko funktsiyakh”, Vestnik Moskovskogo Universiteta. Ser. 15, 2021 (to appear) text
22. V. N. Potapov, S. V. Avgustinovich, Siberian Math. J., 61:5 (2020), 867–877  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
23. V. N. Potapov, “On q-ary bent and plateaued functions”, Des. Codes Cryptography, 88:10 (2020), 2037–2049 , arXiv: 1911.06973  crossref  mathscinet  zmath  isi  scopus 2
24. V. N. Potapov, “Constructions of pairs of orthogonal latin cubes”, Journal of Combinatorial Designs, 28:8 (2020), 604–613 , arXiv: 1911.12960  crossref  mathscinet  isi  scopus 7
25. 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  mathnet  crossref  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  scopus
26. 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  crossref  mathscinet  zmath  isi  scopus 4
27. 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  mathscinet  zmath  scopus
28. 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  crossref  isi  scopus 1
29. 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  crossref  scopus 2
30. 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  crossref  scopus
31. Vladimir N. Potapov, “Partial covering arrays for data hiding and quantization”, Sib. elektron. matem. izv., 15 (2018), 561–569  mathnet  crossref  mathscinet  zmath  isi  scopus
32. V. N. Potapov, “On the number of SQSs, latin hypercubes and MDS codes”, Journal of Combinatorial Designs, 26:5 (2018), 237–248  crossref  mathscinet  zmath  isi  scopus 4
33. 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  crossref  mathscinet  zmath  isi  elib  scopus 23
34. D. S. Krotov, V. N. Potapov, “Constructions of transitive latin hypercubes”, European Journal of Combinatorics, 54:1 (2016), 51–64  crossref  mathscinet  zmath  isi  scopus 1
35. S. Avgustinovich , S. Kitaev, V. N. Potapov, V. Vajnovszki, “Gray coding cubic planar maps”, Theoret. Comput. Sci., 616 (2016), 59–69  crossref  mathscinet  zmath  isi  elib  scopus 1
36. V. N. Potapov, “On the number of transversals in latin squares”, Discrete Appl. Math., 202 (2016), 194–196  crossref  mathscinet  zmath  isi  elib  scopus 2
37. 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  crossref  isi  scopus
38. 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  crossref  isi  scopus 6
39. 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  mathnet  crossref
40. V. N. Potapov, “On the multidimensional permanent and $q$-ary designs”, Sib. Èlektron. Mat. Izv., 11 (2014), 451–456  mathnet  mathscinet  zmath  isi  elib  scopus
41. D. S. Krotov, V. N. Potapov, “Propelinear 1-perfect codes from quadratic functions”, IEEE Trans. Inform. Theory, 60:4 (2014), 2065–2068  crossref  mathscinet  zmath  isi  elib  scopus 4
42. 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  crossref  isi  scopus 3
43. V. N. Potapov, Vvedenie v teoriyu informatsii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2014 , 152 pp.
44. V. N. Potapov, “Infinite-Dimensional Quasigroups of Finite Orders”, Math. Notes, 93:3 (2013), 479–486  mathnet  crossref  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
45. V. N. Potapov, “Multidimensional Latin bitrades”, Siberian Math. J., 54:2 (2013), 317–324  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
46. 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  crossref  isi  scopus
47. 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  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
48. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
49. V. N. Potapov, “On almost balanced Boolean functions”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 23–25  mathnet
50. 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  mathnet  crossref  mathscinet  mathscinet  zmath  zmath  isi  elib  scopus
51. V. N. Potapov, “On perfect 2-colorings of the q-ary n-cube”, Discrete Math., 312:6 (2012), 1269–1272  crossref  mathscinet  zmath  isi  elib  scopus 11
52. V. N. Potapov, “On extensions of partial $n$-quasigroups of order 4”, Siberian Adv. Math., 22:2 (2012), 135–151  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
53. V. N. Potapov, “On perfect 2-colorings of the $q$-ary hypercube”, Prikl. Diskr. Mat., 2011, no. supplement № 4, 18–20  mathnet
54. V. N. Potapov, “Clique matchings in the $k$-ary $n$-dimensional cube”, Siberian Math. J., 52:2 (2011), 303–310  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
55. 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  crossref  mathscinet  zmath  isi  elib  scopus 5
56. 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  elib  scopus
57. 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  mathnet  mathscinet  zmath  isi  elib
58. D. S. Krotov, V. N. Potapov, “n-Ary quasigroups of order 4”, SIAM J. Discrete Math., 23:2 (2009), 561–570  crossref  mathscinet  zmath  isi  elib  scopus 24
59. 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.  mathscinet
60. V. N. Potapov, “Arithmetic coding of messages using random sequence”, Prikl. Diskr. Mat., 2008, no. 2(2), 131–133  mathnet  zmath  elib
61. 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  mathscinet  zmath
62. 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.  mathscinet
63. D. C. Krotov, V. N. Potapov, “Konstruktsii n-kvazigrupp”, Vestnik TGU. Prilozhenie, 23 (2007), 35–36
64. V. N. Potapov, “A lower bound for the number of transitive perfect codes”, J. Appl. Industr. Math., 1:3 (2007), 373–379  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
65. V. N. Potapov, D. S. Krotov, “Asymptotics for the number of $n$-quasigroups of order 4”, Siberian Math. J., 47:4 (2006), 720–731  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
66. 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  mathnet  mathscinet
67. V. N. Potapov, “Additive complexity of words with restrictions on the composition of subwords”, Diskretn. Anal. Issled. Oper., 11:1 (2004), 52–78  mathnet  mathscinet  zmath
68. 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  mathnet  crossref  mathscinet  zmath  scopus
69. Y. L. Orlov, V. N. Potapov, “Complexity: an internet resource for analysis of DNA sequence complexity”, Nucl. Acids. Res., 32 (2004), 628–633  crossref  isi  scopus 70
70. 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  crossref  mathscinet  isi  scopus 6
71. 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  scopus
72. 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  mathnet  mathscinet  zmath
73. V. N. Potapov, “Numeratsiya tselochislennogo simpleksa”, Vestnik NNGU. Matematicheskoe modelirovanie i optimalnoe upravlenie, 22:1 (2000), 152–158  zmath
74. Yu. L. Orlov, V. N. Potapov, “Otsenka stokhasticheskoi slozhnosti geneticheskikh tekstov”, Vychislitelnye tekhnologii, 5, spetsvypusk (2000), 5–15
75. V. N. Potapov, “A survey of methods for the undistorted coding of discrete sources”, Diskretn. Anal. Issled. Oper., 6:4 (1999), 49–91  mathnet  mathscinet  zmath
76. 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  mathnet  mathscinet  zmath
77. R. E. Krichevskii, V. N. Potapov, “Rapid encoding of run lengths and pyramid cubic lattices”, IEEE Trans. Inform. Theory, 45:4 (1999), 1347–1350  crossref  mathscinet  zmath  isi  scopus 1
78. V. N. Potapov, Teoriya informatsii. Kodirovanie diskretnykh veroyatnostnykh istochnikov, Izd. tsentr NGU, 1999 , 71 pp.
79. V. N. Potapov, “$\varepsilon$-entropy of compacta in $C$, and tabulation of continuous functions”, Siberian Math. J., 38:4 (1997), 759–771  mathnet  crossref  mathscinet  zmath  isi  scopus
80. 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  crossref  scopus
81. R. E. Krichevskii, V. N. Potapov, “Compression and restoration of square integrable function”, Electron. Res. Announc. Amer. Math. Soc., 2:1 (1996), 42–49  crossref  mathscinet  zmath
82. V. N. Potapov, “Tabulirovanie gladkikh funktsii”, Mezhvuz. sb. nauch. tr. Analiz i diskretnaya matematika, NGU, Novosibirsk, 1995, 115–125  mathscinet
83. 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  crossref  isi  scopus
84. R. E. Krichevskii, V. N. Potapov, “Combinatorial Source Encoding and Perfect Hashing”, Proceedings of 1994 IEEE International Symposium on Information Theory, IEEE, 1994, 319  crossref  scopus
85. V. N. Potapov, “Fast lexicographic search”, Dokl. Math., 47:3 (1993), 431–434  mathnet  mathscinet  isi

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   

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