Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices.

Vladimir N. Potapov Sobolev Institute of Mathematics, Novosibirsk, Russia http://math.nsc.ru/~potapov/maineng.htm https://scholar.google.com/citations?user=0DynDV0AAAAJ https://orcid.org/0000-0001-9461-2064 https://www.scopus.com/authid/detail.uri?authorId=7102561165

Vladimir N. Potapov Anna A. Taranenko Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices. 114653 2026 349 Discret. Math. 1 https://doi.org/10.1016/j.disc.2025.114653 db/journals/dm/dm349.html#PotapovT26 streams/journals/dm

Denis S. Krotov Ferruh Özbudak Vladimir N. Potapov Generalizing the Bierbrauer-Friedman bound for orthogonal arrays. 4937-4950 2025 November 93 Des. Codes Cryptogr. 11 https://doi.org/10.1007/s10623-025-01711-y db/journals/dcc/dcc93.html#KrotovOP25 streams/journals/dcc

Vladimir N. Potapov Ferruh Özbudak Asymptotic bounds on the numbers of certain bent functions. 1289-1307 2024 November 16 Cryptogr. Commun. 6 https://doi.org/10.1007/s12095-024-00726-x db/journals/ccds/ccds16.html#PotapovO24 streams/journals/ccds

Vladimir N. Potapov Anna A. Taranenko Yuriy V. Tarannikov An asymptotic lower bound on the number of bent functions. 639-651 2024 March 92 Des. Codes Cryptogr. 3 https://doi.org/10.1007/s10623-023-01239-z db/journals/dcc/dcc92.html#PotapovTT24

Denis S. Krotov Vladimir N. Potapov An upper bound on the number of frequency hypercubes. 113657 2024 January 347 Discret. Math. 1 https://doi.org/10.1016/j.disc.2023.113657 db/journals/dm/dm347.html#KrotovP24

Sergey V. Avgustinovich Sergey Kitaev Jeffrey Liese Vladimir N. Potapov Anna A. Taranenko Singleton mesh patterns in multidimensional permutations. 105801 2024 January 201 J. Comb. Theory A https://doi.org/10.1016/j.jcta.2023.105801 db/journals/jcta/jcta201.html#AvgustinovichKLPT24

Denis S. Krotov Ferruh Özbudak Vladimir N. Potapov Generalizing the Bierbrauer-Friedman bound. 2024 abs/2411.16559 CoRR https://doi.org/10.48550/arXiv.2411.16559 db/journals/corr/corr2411.html#abs-2411-16559 streams/journals/corr

Vladimir N. Potapov Upper bounds on the numbers of binary plateaued and bent functions. 2023 abs/2303.16547 CoRR https://doi.org/10.48550/arXiv.2303.16547 db/journals/corr/corr2303.html#abs-2303-16547

Vladimir N. Potapov Existence of balanced functions that are not derivative of bent functions. 2023 abs/2309.04244 CoRR https://doi.org/10.48550/arXiv.2309.04244 db/journals/corr/corr2309.html#abs-2309-04244

A. L. Perezhogin Vladimir N. Potapov S. Yu. Vladimirov Every latin hypercube of order 5 has transversals. 2023 abs/2311.14997 CoRR https://doi.org/10.48550/arXiv.2311.14997 db/journals/corr/corr2311.html#abs-2311-14997

Vladimir N. Potapov DP-Colorings of Uniform Hypergraphs and Splittings of Boolean Hypercube into Faces. 2022 29 Electron. J. Comb. 3 https://doi.org/10.37236/10550 db/journals/combinatorics/combinatorics29.html#Potapov22

Denis S. Krotov Vladimir N. Potapov An upper bound on the number of frequency hypercubes. 2022 abs/2212.03694 CoRR https://doi.org/10.48550/arXiv.2212.03694 db/journals/corr/corr2212.html#abs-2212-03694

Denis S. Krotov Vladimir N. Potapov On Multifold Packings of Radius-1 Balls in Hamming Graphs. 3585-3598 2021 67 IEEE Trans. Inf. Theory 6 https://doi.org/10.1109/TIT.2020.3046260 db/journals/tit/tit67.html#KrotovP21

Vladimir N. Potapov An Upper Bound on the Number of Bent Functions. 95-96 2021 REDUNDANCY https://doi.org/10.1109/REDUNDANCY52534.2021.9606445 conf/redundancy/2021 db/conf/redundancy/redundancy2021.html#Potapov21 Vladimir N. Potapov On Weight Spectrum of Linear Codes. 116-118 2021 REDUNDANCY https://doi.org/10.1109/REDUNDANCY52534.2021.9606478 conf/redundancy/2021 db/conf/redundancy/redundancy2021.html#Potapov21a

Vladimir N. Potapov On weight spectrum of linear codes. 2021 abs/2107.14576 CoRR https://arxiv.org/abs/2107.14576 db/journals/corr/corr2107.html#abs-2107-14576

Vladimir N. Potapov An Upper Bound on the Number of Bent Functions. 2021 abs/2107.14583 CoRR https://arxiv.org/abs/2107.14583 db/journals/corr/corr2107.html#abs-2107-14583

Vladimir N. Potapov On q-ary bent and plateaued functions. 2037-2049 2020 88 Des. Codes Cryptogr. 10 https://doi.org/10.1007/s10623-020-00761-8 db/journals/dcc/dcc88.html#Potapov20

Vladimir N. Potapov Graeco-Latin cubes. 2020 December https://doi.org/10.21227/xh3k-pv95 IEEE DataPort streams/repo/ieeedataport

Sergey Kitaev Vladimir N. Potapov Vincent Vajnovszki On shortening u-cycles and u-words for permutations. 203-213 2019 260 Discret. Appl. Math. https://doi.org/10.1016/j.dam.2019.01.025 db/journals/dam/dam260.html#KitaevPV19

Denis S. Krotov Vladimir N. Potapov On the Cardinality Spectrum and the Number of Latin Bitrades of Order 3. 343-365 2019 55 Probl. Inf. Transm. 4 https://doi.org/10.1134/S0032946019040021 https://www.wikidata.org/entity/Q126289364 db/journals/poit/poit55.html#KrotovP19

Denis S. Krotov Vladimir N. Potapov On two-fold packings of radius-1 balls in Hamming graphs. 2773-2777 2019 ISIT https://doi.org/10.1109/ISIT.2019.8849832 conf/isit/2019 db/conf/isit/isit2019.html#KrotovP19 Vladimir N. Potapov On Minimal Distance between q-ary Plateaued Functions. 42-44 2019 REDUNDANCY https://doi.org/10.1109/REDUNDANCY48165.2019.9003309 conf/redundancy/2019 db/conf/redundancy/redundancy2019.html#Potapov19 Vladimir N. Potapov A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity. 45-46 2019 REDUNDANCY https://doi.org/10.1109/REDUNDANCY48165.2019.9003342 conf/redundancy/2019 db/conf/redundancy/redundancy2019.html#Potapov19a

Denis S. Krotov Vladimir N. Potapov On two-fold packings of radius-1 balls in Hamming graphs. 2019 abs/1902.00023 CoRR http://arxiv.org/abs/1902.00023 db/journals/corr/corr1902.html#abs-1902-00023

Denis S. Krotov Evgeny V. Gorkunov Vladimir N. Potapov On the number of autotopies of an n-ary qusigroup of order 4. 2019 abs/1903.00188 CoRR http://arxiv.org/abs/1903.00188 db/journals/corr/corr1903.html#abs-1903-00188

Vladimir N. Potapov A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity. 2019 abs/1910.02621 CoRR http://arxiv.org/abs/1910.02621 db/journals/corr/corr1910.html#abs-1910-02621

Vladimir N. Potapov On q-ary Bent and Plateaued Functions. 2019 abs/1911.06973 CoRR http://arxiv.org/abs/1911.06973 db/journals/corr/corr1911.html#abs-1911-06973

Vladimir N. Potapov Constructions of Pairs of Orthogonal Latin Cubes. 2019 abs/1911.12960 CoRR http://arxiv.org/abs/1911.12960 db/journals/corr/corr1911.html#abs-1911-12960

Vladimir N. Potapov On the number of transversals in latin squares. 194-196 2016 202 Discret. Appl. Math. https://doi.org/10.1016/j.dam.2015.08.005 db/journals/dam/dam202.html#Potapov16

Denis S. Krotov Ivan Yu. Mogilnykh Vladimir N. Potapov To the theory of q-ary Steiner and other-type trades. 1150-1157 2016 339 Discret. Math. 3 https://doi.org/10.1016/j.disc.2015.11.002 db/journals/dm/dm339.html#KrotovMP16

Denis S. Krotov Vladimir N. Potapov Constructions of transitive latin hypercubes. 51-64 2016 54 Eur. J. Comb. https://doi.org/10.1016/j.ejc.2015.12.001 db/journals/ejc/ejc54.html#KrotovP16

Sergey V. Avgustinovich Sergey Kitaev Vladimir N. Potapov Vincent Vajnovszki Gray coding cubic planar maps. 59-69 2016 616 Theor. Comput. Sci. https://doi.org/10.1016/j.tcs.2015.12.013 db/journals/tcs/tcs616.html#AvgustinovichKP16

Vladimir N. Potapov On minimal distance between q-ary bent functions. 2016 abs/1606.02430 CoRR http://arxiv.org/abs/1606.02430 db/journals/corr/corr1606.html#Potapov16a

Sergey V. Avgustinovich Sergey Kitaev Vladimir N. Potapov Vincent Vajnovszki Gray coding planar maps. 2015 abs/1509.05807 CoRR http://arxiv.org/abs/1509.05807 db/journals/corr/corr1509.html#AvgustinovichKP15

Vladimir N. Potapov Linear codes for an effective quantization of data. 2015 abs/1512.09287 CoRR http://arxiv.org/abs/1512.09287 db/journals/corr/corr1512.html#Potapov15

Denis S. Krotov Vladimir N. Potapov Propelinear 1-Perfect Codes From Quadratic Functions. 2065-2068 2014 60 IEEE Trans. Inf. Theory 4 https://doi.org/10.1109/TIT.2014.2303158 db/journals/tit/tit60.html#KrotovP14

Alexey Filippov Vasily Rufitskiy Vladimir N. Potapov Scalar-quantization-based multi-layer data hiding for video coding applications. 262-265 2014 VCIP https://doi.org/10.1109/VCIP.2014.7051554 conf/vcip/2014 db/conf/vcip/vcip2014.html#FilippovRP14 Vladimir N. Potapov Nikolay Shlyakhov Albert Silantiev Mikhail Tchobanou What could be after HEVC? 1-5 2013 ICICS https://doi.org/10.1109/ICICS.2013.6782938 conf/IEEEicics/2013 db/conf/IEEEicics/IEEEicics2013.html#PotapovSST13

Denis S. Krotov Vladimir N. Potapov Transitive 1-perfect codes from quadratic functions http://arxiv.org/abs/1301.0014 2013 CoRR abs/1301.0014 db/journals/corr/corr1301.html#abs-1301-0014

Denis S. Krotov Vladimir N. Potapov Construction of transitive MDS codes http://arxiv.org/abs/1303.0004 2013 CoRR abs/1303.0004 db/journals/corr/corr1303.html#abs-1303-0004

Vladimir N. Potapov On perfect 2-colorings of the q-ary n-cube. 1269-1272 2012 312 Discret. Math. 6 https://doi.org/10.1016/j.disc.2011.12.004 db/journals/dm/dm312.html#Potapov12

Vladimir N. Potapov Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes. 47-55 2012 48 Probl. Inf. Transm. 1 https://doi.org/10.1134/S003294601201005X db/journals/poit/poit48.html#Potapov12

Denis S. Krotov Vladimir N. Potapov On connection between reducibility of an n-ary quasigroup and that of its retracts. 58-66 2011 311 Discret. Math. 1 https://doi.org/10.1016/j.disc.2010.09.023 db/journals/dm/dm311.html#KrotovP11

Denis S. Krotov Vladimir N. Potapov On switching equivalence of <i>n</i>-ary quasigroups of order 4 and perfect binary codes. 219-224 2010 46 Probl. Inf. Transm. 3 https://doi.org/10.1134/S0032946010030026 db/journals/poit/poit46.html#KrotovP10

Denis S. Krotov Vladimir N. Potapov n-Ary Quasigroups of Order 4. 561-570 2009 23 SIAM J. Discret. Math. 2 https://doi.org/10.1137/070697331 db/journals/siamdm/siamdm23.html#KrotovP09

Vladimir N. Potapov Redundancy estimates for the Lempel-Ziv algorithm of data compression. 245-254 2004 135 Discret. Appl. Math. 1-3 https://doi.org/10.1016/S0166-218X(02)00308-6 db/journals/dam/dam135.html#Potapov04

Yuri L. Orlov Vladimir N. Potapov Complexity: an internet resource for analysis of DNA sequence complexity. 628-633 2004 32 Nucleic Acids Res. Web-Server-Issue db/journals/nar/nar32.html#OrlovP04 https://doi.org/10.1093/nar/gkh466 https://www.wikidata.org/entity/Q34328904

Denis S. Krotov Vladimir N. Potapov On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes. 5-12 2004 40 Probl. Inf. Transm. 1 https://doi.org/10.1023/B%3APRIT.0000024875.79605.fc db/journals/poit/poit40.html#KrotovP04

Yuri L. Orlov Vladimir D. Gusev Lubov A. Nemytikova Vladimir N. Potapov Nadia A. Kolchanov Internet-Available Software Packages for Analysis of DNA Sequence Complexity. 35-38 2003 conf/metmbs/2003 METMBS db/conf/metmbs/metmbs2003.html#OrlovGNPK03

Yuri L. Orlov V. P. Filippov Vladimir N. Potapov Nikolay A. Kolchanov Construction of stochastic context trees for genetical texts. 233-247 2002 2 Silico Biol. 3 http://content.iospress.com/articles/in-silico-biology/isb00045 http://www.bioinfo.de/isb/abstracts/02/0022.html db/journals/isb/isb2.html#OrlovFPK02

Yuri L. Orlov V. P. Filippov Vladimir N. Potapov Nikolay A. Kolchanov Construction of stochastic context trees for genetical texts. 212-215 2001 conf/gcb/2001 German Conference on Bioinformatics db/conf/gcb/gcb2001.html#OrlovFPK01

Rafail E. Krichevskiy Vladimir N. Potapov Rapid Encoding of Run Lengths and Pyramid Cubic Lattices. 1347-1350 1999 45 IEEE Trans. Inf. Theory 4 db/journals/tit/tit45.html#KrichevskiyP99 https://doi.org/10.1109/18.761300

Sergey V. Avgustinovich Alexey Filippov V. P. Filippov Evgeny V. Gorkunov Vladimir D. Gusev Sergey Kitaev Nadia A. Kolchanov Nikolay A. Kolchanov Rafail E. Krichevskiy Denis S. Krotov Jeffrey Liese Ivan Yu. Mogilnykh Lubov A. Nemytikova Yuriy L. OrlovYuri L. Orlov Ferruh Özbudak A. L. Perezhogin Vasily Rufitskiy Nikolay Shlyakhov Albert Silantiev Anna A. Taranenko Yuriy V. Tarannikov Mikhail Tchobanou Vincent Vajnovszki S. Yu. Vladimirov