Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs.

Ivan Yu. Mogilnykh Novosibirsk State University, Russia Sobolev Institute of Mathematics, Novosibirsk, Russia https://orcid.org/0000-0003-3770-8523

Ivan Yu. Mogilnykh Anna A. Taranenko Konstantin V. Vorob'ev Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs. 114296 2025 348 Discret. Math. 2 https://doi.org/10.1016/j.disc.2024.114296 db/journals/dm/dm348.html#MogilnykhTV25 streams/journals/dm

Denis S. Krotov Ivan Yu. Mogilnykh Multispreads. 102675 2025 108 Finite Fields Their Appl. https://doi.org/10.1016/j.ffa.2025.102675 db/journals/ffa/ffa108.html#KrotovM25 streams/journals/ffa

Ivan Yu. Mogilnykh Anastasia Yu. Vasil'eva On null completely regular codes in Manhattan metric. 2025 May abs/2505.09893 CoRR https://doi.org/10.48550/arXiv.2505.09893 db/journals/corr/corr2505.html#abs-2505-09893 streams/journals/corr

Alexey D. Marin Ivan Yu. Mogilnykh Binary codes from subset inclusion matrices. 2024 abs/2408.12154 CoRR https://doi.org/10.48550/arXiv.2408.12154 db/journals/corr/corr2408.html#abs-2408-12154 streams/journals/corr

Ivan Yu. Mogilnykh Konstantin V. Vorob'ev On completely regular codes with minimum eigenvalue in geometric graphs. 113357 2023 July 346 Discret. Math. 7 https://doi.org/10.1016/j.disc.2023.113357 db/journals/dm/dm346.html#MogilnykhV23

Ivan Yu. Mogilnykh Faina I. Solov'eva Constructions and Invariants of Optimal Codes in the Lee Metric. 71-85 2023 July 59 Probl. Inf. Transm. 2 https://doi.org/10.1134/S0032946023020011 db/journals/poit/poit59.html#MogilnykhS23

E. A. Bespalov Ivan Yu. Mogilnykh Konstantin V. Vorob'ev L<sub>∞</sub> norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs. 2023 abs/2304.00922 CoRR https://doi.org/10.48550/arXiv.2304.00922 db/journals/corr/corr2304.html#abs-2304-00922

Denis S. Krotov Ivan Yu. Mogilnykh Multispreads. 2023 abs/2312.07883 CoRR https://doi.org/10.48550/arXiv.2312.07883 db/journals/corr/corr2312.html#abs-2312-07883

Ivan Yu. Mogilnykh Completely Regular Codes in Johnson and Grassmann Graphs with Small Covering Radii. 2022 29 Electron. J. Comb. 2 https://doi.org/10.37236/10083 db/journals/combinatorics/combinatorics29.html#Mogilnykh22

Ivan Yu. Mogilnykh On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group. 58-71 2022 58 Probl. Inf. Transm. 1 https://doi.org/10.1134/S0032946022010045 db/journals/poit/poit58.html#Mogilnykh22

Ivan Yu. Mogilnykh Faina I. Solov'eva On Weight Distributions for a Class of Codes with Parameters of Reed-Muller Codes. 231-241 2022 58 Probl. Inf. Transm. 3 https://doi.org/10.1134/S0032946022030036 db/journals/poit/poit58.html#MogilnykhS22

Ivan Yu. Mogilnykh Konstantin V. Vorob'ev On completely regular codes with minimum eigenvalue in geometric graphs. 2022 abs/2210.11184 CoRR https://doi.org/10.48550/arXiv.2210.11184 db/journals/corr/corr2210.html#abs-2210-11184

Ivan Yu. Mogilnykh q-ary Propelinear Perfect Codes from the Regular Subgroups of the GA(r, q) and Their Ranks. 2021 abs/2112.08659 CoRR https://arxiv.org/abs/2112.08659 db/journals/corr/corr2112.html#abs-2112-08659

Ivan Yu. Mogilnykh Faina I. Solov'eva On components of the Kerdock codes and the dual of the BCH code C1, 3. 111668 2020 343 Discret. Math. 2 https://doi.org/10.1016/j.disc.2019.111668 db/journals/dm/dm343.html#MogilnykhS20

Ivan Yu. Mogilnykh Alexandr Valyuzhenich Equitable 2-partitions of the Hamming graphs with the second eigenvalue. 112039 2020 343 Discret. Math. 11 https://doi.org/10.1016/j.disc.2020.112039 db/journals/dm/dm343.html#MogilnykhV20

Ivan Yu. Mogilnykh Faina I. Solov'eva On existence of perfect bitrades in Hamming graphs. 112128 2020 343 Discret. Math. 12 https://doi.org/10.1016/j.disc.2020.112128 db/journals/dm/dm343.html#MogilnykhS20a

Ivan Yu. Mogilnykh Faina I. Solov'eva On Bases of BCH Codes with Designed Distance 3 and Their Extensions. 309-316 2020 56 Probl. Inf. Transm. 4 https://doi.org/10.1134/S003294602004002X db/journals/poit/poit56.html#MogilnykhS20

Ivan Yu. Mogilnykh Faina I. Solov'eva Single orbit affine generators for extended BCH codes with designed distance three. 1-3 2020 ACCT https://doi.org/10.1109/ACCT51235.2020.9383376 conf/acct/2020 db/conf/acct/acct2020.html#MogilnykhS20

Ivan Yu. Mogilnykh Faina I. Solov'eva Coordinate transitivity of extended perfect codes and their SQS. 2020 abs/2009.08191 CoRR https://arxiv.org/abs/2009.08191 db/journals/corr/corr2009.html#abs-2009-08191

Ivan Yu. Mogilnykh Completely regular codes in Johnson and Grassmann graphs with small covering radii. 2020 abs/2012.06970 CoRR https://arxiv.org/abs/2012.06970 db/journals/corr/corr2012.html#abs-2012-06970

Ivan Yu. Mogilnykh Faina I. Solov'eva A concatenation construction for propelinear perfect codes from regular subgroups of GA(r, 2). 2019 abs/1905.10005 CoRR http://arxiv.org/abs/1905.10005 db/journals/corr/corr1905.html#abs-1905-10005

Ivan Yu. Mogilnykh Faina I. Solov'eva On existence of perfect bitrades in Hamming graphs. 2019 abs/1912.09089 CoRR http://arxiv.org/abs/1912.09089 db/journals/corr/corr1912.html#abs-1912-09089

Ivan Yu. Mogilnykh Faina I. Solov'eva On explicit minimum weight bases for extended cyclic codes related to Gold functions. 2619-2627 2018 86 Des. Codes Cryptogr. 11 https://doi.org/10.1007/s10623-018-0464-7 db/journals/dcc/dcc86.html#MogilnykhS18

Konstantin V. Vorob'ev Ivan Yu. Mogilnykh Alexandr Valyuzhenich Minimum supports of eigenfunctions of Johnson graphs. 2151-2158 2018 341 Discret. Math. 8 https://doi.org/10.1016/j.disc.2018.04.018 db/journals/dm/dm341.html#VorobevMV18

Ivan Yu. Mogilnykh A note on regular subgroups of the automorphism group of the linear Hadamard code. 2018 abs/1807.04446 CoRR http://arxiv.org/abs/1807.04446 db/journals/corr/corr1807.html#abs-1807-04446

Ivan Yu. Mogilnykh Faina I. Solov'eva On components of a Kerdock code and the dual of the BCH code C<sub>1, 3</sub>. 2018 abs/1810.04367 CoRR http://arxiv.org/abs/1810.04367 db/journals/corr/corr1810.html#abs-1810-04367

Denis S. Krotov Ivan Yu. Mogilnykh Anastasia Yu. Vasil'eva On completely regular codes of covering radius 1 in the halved hypercubes. 2018 abs/1812.03159 CoRR http://arxiv.org/abs/1812.03159 db/journals/corr/corr1812.html#abs-1812-03159

Ivan Yu. Mogilnykh Faina I. Solov'eva Propelinear codes related to some classes of optimal codes. 251-259 2017 53 Probl. Inf. Transm. 3 https://doi.org/10.1134/S0032946017030061 db/journals/poit/poit53.html#MogilnykhS17

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

Ivan Yu. Mogilnykh Faina I. Solov'eva On the symmetry group of the Mollard code. 265-275 2016 52 Probl. Inf. Transm. 3 https://doi.org/10.1134/S0032946016030042 db/journals/poit/poit52.html#MogilnykhS16

Ivan Yu. Mogilnykh On extending propelinear structures of the Nordstrom-Robinson code to the Hamming code. 289-298 2016 52 Probl. Inf. Transm. 3 https://doi.org/10.1134/S0032946016030078 db/journals/poit/poit52.html#Mogilnykh16

Ivan Yu. Mogilnykh Faina I. Solov'eva Transitive nonpropelinear perfect codes. 174-182 2015 338 Discret. Math. 3 https://doi.org/10.1016/j.disc.2014.11.001 db/journals/dm/dm338.html#MogilnykhS15

Ivan Yu. Mogilnykh Faina I. Solov'eva On separability of the classes of homogeneous and transitive perfect binary codes. 139-147 2015 51 Probl. Inf. Transm. 2 https://doi.org/10.1134/S0032946015020054 db/journals/poit/poit51.html#MogilnykhS15

Ivan Yu. Mogilnykh Faina I. Solov'eva On maximum components of a class of perfect codes. 2015 abs/1512.03242 CoRR http://arxiv.org/abs/1512.03242 db/journals/corr/corr1512.html#MogilnykhS15

Ivan Yu. Mogilnykh On the extention of propelinear structures of Nordstrom-Robinson code to Hamming code. 2015 abs/1512.03245 CoRR http://arxiv.org/abs/1512.03245 db/journals/corr/corr1512.html#Mogilnykh15

Alexander L. Gavrilyuk Ivan Yu. Mogilnykh Cameron-Liebler line classes in PG(n, 4). 969-982 2014 73 Des. Codes Cryptogr. 3 https://doi.org/10.1007/s10623-013-9838-z db/journals/dcc/dcc73.html#GavrilyukM14

Joaquim Borges Ivan Yu. Mogilnykh Josep Rifà Faina I. Solov'eva On the Number of Nonequivalent Propelinear Extended Perfect Codes. 37 2013 20 Electron. J. Comb. 2 https://doi.org/10.37236/3220 db/journals/combinatorics/combinatorics20.html#BorgesMRS13

George K. Guskov Ivan Yu. Mogilnykh Faina I. Solov'eva Rank spectrum of propelinear perfect binary codes. 879-881 2013 ISIT https://doi.org/10.1109/ISIT.2013.6620352 conf/isit/2013 db/conf/isit/isit2013.html#GuskovMS13

Joaquim Borges Ivan Yu. Mogilnykh Josep Rifà Faina I. Solov'eva Structural properties of binary propelinear codes. 329-346 2012 6 Adv. Math. Commun. 3 https://doi.org/10.3934/amc.2012.6.329 db/journals/amco/amco6.html#BorgesMRS12

George K. Guskov Ivan Yu. Mogilnykh Faina I. Solov'eva Ranks of propelinear perfect binary codes http://arxiv.org/abs/1210.8253 2012 CoRR abs/1210.8253 db/journals/corr/corr1210.html#abs-1210-8253

Ivan Yu. Mogilnykh On weak isometries of Preparata codes. 145-150 2009 45 Probl. Inf. Transm. 2 https://doi.org/10.1134/S0032946009020057 db/journals/poit/poit45.html#Mogilnykh09

Ivan Yu. Mogilnykh Patric R. J. Östergård Olli Pottonen Faina I. Solov'eva Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs. 2622-2625 2009 55 IEEE Trans. Inf. Theory 6 https://doi.org/10.1109/TIT.2009.2018338 db/journals/tit/tit55.html#MogilnykhOPS09

Ivan Yu. Mogilnykh On weak isometries of Preparata codes http://arxiv.org/abs/0902.2316 2009 CoRR abs/0902.2316 db/journals/corr/corr0902.html#abs-0902-2316

Sergey V. Avgustinovich Ivan Yu. Mogilnykh Perfect 2-Colorings of Johnson Graphs J(6, 3) and J(7, 3). 11-19 2008 ICMCTA https://doi.org/10.1007/978-3-540-87448-5_2 conf/icmcta/2008 db/conf/icmcta/icmcta2008.html#AvgustinovichM08

Ivan Yu. Mogilnykh Patric R. J. Östergård Olli Pottonen Faina I. Solov'eva Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs http://arxiv.org/abs/0810.5633 2008 CoRR abs/0810.5633 db/journals/corr/corr0810.html#abs-0810-5633

Ivan Yu. Mogilnykh On the regularity of perfect 2-colorings of the Johnson graph. 303-309 2007 43 Probl. Inf. Transm. 4 https://doi.org/10.1134/S0032946007040035 db/journals/poit/poit43.html#Mogilnykh07

Sergey V. Avgustinovich E. A. Bespalov Joaquim Borges Alexander L. Gavrilyuk George K. Guskov Denis S. Krotov Alexey D. Marin Patric R. J. Östergård Vladimir N. Potapov Olli Pottonen Josep Rifà Faina I. Solov'eva Anna A. Taranenko Alexandr Valyuzhenich Anastasia Yu. Vasil'eva Konstantin V. Vorob'ev