Krotov, Denis S.; Potapov, Vladimir N. An upper bound on the number of frequency hypercubes. (English) Zbl 1525.05015 Discrete Math. 347, No. 1, Article ID 113657, 9 p. (2024). MSC: 05B15 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{V. N. Potapov}, Discrete Math. 347, No. 1, Article ID 113657, 9 p. (2024; Zbl 1525.05015) Full Text: DOI arXiv
Krotov, Denis S. Projective tilings and full-rank perfect codes. (English) Zbl 1525.94068 Des. Codes Cryptography 91, No. 10, 3293-3303 (2023). Reviewer: Nikolay Yankov (Shumen) MSC: 94B25 05B45 PDFBibTeX XMLCite \textit{D. S. Krotov}, Des. Codes Cryptography 91, No. 10, 3293--3303 (2023; Zbl 1525.94068) Full Text: DOI arXiv
Shi, Minjia; Xia, Yuhong; Krotov, Denis S. A family of diameter perfect constant-weight codes from Steiner systems. (English) Zbl 07730227 J. Comb. Theory, Ser. A 200, Article ID 105790, 20 p. (2023). MSC: 94Bxx 05Bxx 05Cxx PDFBibTeX XMLCite \textit{M. Shi} et al., J. Comb. Theory, Ser. A 200, Article ID 105790, 20 p. (2023; Zbl 07730227) Full Text: DOI arXiv
Shi, Minjia; Krotov, Denis S. An enumeration of 1-perfect ternary codes. (English) Zbl 1519.94239 Discrete Math. 346, No. 7, Article ID 113437, 16 p. (2023). Reviewer: Nikolay Yankov (Shumen) MSC: 94B05 PDFBibTeX XMLCite \textit{M. Shi} and \textit{D. S. Krotov}, Discrete Math. 346, No. 7, Article ID 113437, 16 p. (2023; Zbl 1519.94239) Full Text: DOI arXiv
Krotov, Denis S. Perfect colorings of the infinite square grid: coverings and twin colors. (English) Zbl 1511.05079 Electron. J. Comb. 30, No. 2, Research Paper P2.4, 59 p. (2023). MSC: 05C15 05C70 05B05 05B30 PDFBibTeX XMLCite \textit{D. S. Krotov}, Electron. J. Comb. 30, No. 2, Research Paper P2.4, 59 p. (2023; Zbl 1511.05079) Full Text: DOI arXiv
Shi, Minjia; Krotov, Denis S.; Solé, Patrick On the coset graph construction of distance-regular graphs. (English) Zbl 1527.05181 Discrete Math. 345, No. 11, Article ID 113037, 6 p. (2022). MSC: 05E30 05C12 94B15 PDFBibTeX XMLCite \textit{M. Shi} et al., Discrete Math. 345, No. 11, Article ID 113037, 6 p. (2022; Zbl 1527.05181) Full Text: DOI arXiv
Bespalov, Evgeny A.; Krotov, Denis S.; Matiushev, Aleksandr A.; Taranenko, Anna A.; Vorob’ev, Konstantin V. Perfect 2-colorings of Hamming graphs. (English) Zbl 07799184 J. Comb. Des. 29, No. 6, 367-396 (2021). MSC: 05-XX PDFBibTeX XMLCite \textit{E. A. Bespalov} et al., J. Comb. Des. 29, No. 6, 367--396 (2021; Zbl 07799184) Full Text: DOI arXiv
Shi, M. J.; Wang, S. K.; Li, X. X.; Krotov, D. S. On the number of frequency hypercubes \(F^n(4;2,2) \). (English. Russian original) Zbl 1473.05037 Sib. Math. J. 62, No. 5, 951-962 (2021); translation from Sib. Mat. Zh. 62, No. 5, 1173-1187 (2021). MSC: 05B15 05B30 05A15 94B05 PDFBibTeX XMLCite \textit{M. J. Shi} et al., Sib. Math. J. 62, No. 5, 951--962 (2021; Zbl 1473.05037); translation from Sib. Mat. Zh. 62, No. 5, 1173--1187 (2021) Full Text: DOI arXiv
Shi, Minjia; Xu, Li; Krotov, Denis S. On the number of resolvable Steiner triple systems of small 3-rank. (English) Zbl 1439.05038 Des. Codes Cryptography 88, No. 6, 1037-1046 (2020). MSC: 05B07 05B05 51E10 94B27 PDFBibTeX XMLCite \textit{M. Shi} et al., Des. Codes Cryptography 88, No. 6, 1037--1046 (2020; Zbl 1439.05038) Full Text: DOI arXiv
Krotov, Denis S.; Vorob’ev, Konstantin V. On unbalanced Boolean functions with best correlation immunity. (English) Zbl 07183915 Electron. J. Comb. 27, No. 1, Research Paper P1.45, 24 p. (2020). MSC: 06E30 05B15 05B30 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{K. V. Vorob'ev}, Electron. J. Comb. 27, No. 1, Research Paper P1.45, 24 p. (2020; Zbl 07183915) Full Text: DOI arXiv Link
Ghorbani, Ebrahim; Kamali, Sara; Khosrovshahi, Gholamreza B.; Krotov, Denis On the volumes and affine types of trades. (English) Zbl 1431.05022 Electron. J. Comb. 27, No. 1, Research Paper P1.29, 28 p. (2020). MSC: 05B05 05B15 94B05 94B15 PDFBibTeX XMLCite \textit{E. Ghorbani} et al., Electron. J. Comb. 27, No. 1, Research Paper P1.29, 28 p. (2020; Zbl 1431.05022) Full Text: DOI arXiv Link
Krotov, Denis S. On the \(\mathrm{OA}(1536,13,2,7)\) and related orthogonal arrays. (English) Zbl 1437.05035 Discrete Math. 343, No. 2, Article ID 111659, 11 p. (2020). Reviewer: Peter Horák (Tacoma) MSC: 05B15 06E30 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 343, No. 2, Article ID 111659, 11 p. (2020; Zbl 1437.05035) Full Text: DOI arXiv
Krotov, D. S.; Potapov, V. N. On the cardinality spectrum and the number of Latin bitrades of order 3. (English. Russian original) Zbl 1467.94051 Probl. Inf. Transm. 55, No. 4, 343-365 (2019); translation from Probl. Peredachi Inf. 55, No. 4, 52-75 (2019). MSC: 94B05 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{V. N. Potapov}, Probl. Inf. Transm. 55, No. 4, 343--365 (2019; Zbl 1467.94051); translation from Probl. Peredachi Inf. 55, No. 4, 52--75 (2019) Full Text: DOI arXiv
Shi, Minjia; Krotov, Denis S.; Solé, Patrick A new distance-regular graph of diameter 3 on 1024 vertices. (English) Zbl 1419.05220 Des. Codes Cryptography 87, No. 9, 2091-2101 (2019); correction ibid. 87, No. 9, 2103 (2019). MSC: 05E30 05C12 94B05 PDFBibTeX XMLCite \textit{M. Shi} et al., Des. Codes Cryptography 87, No. 9, 2091--2101 (2019; Zbl 1419.05220) Full Text: DOI arXiv
Shi, Minjia; Huang, Daitao; Krotov, Denis S. Additive perfect codes in Doob graphs. (English) Zbl 1409.94927 Des. Codes Cryptography 87, No. 8, 1857-1869 (2019). MSC: 94B05 94B25 05B40 PDFBibTeX XMLCite \textit{M. Shi} et al., Des. Codes Cryptography 87, No. 8, 1857--1869 (2019; Zbl 1409.94927) Full Text: DOI arXiv
Krotov, Denis S.; Bespalov, Evgeny A. Distance-2 MDS codes and Latin colorings in the Doob graphs. (English) Zbl 1402.05167 Graphs Comb. 34, No. 5, 1001-1017 (2018). MSC: 05C69 05C12 05C35 05B15 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{E. A. Bespalov}, Graphs Comb. 34, No. 5, 1001--1017 (2018; Zbl 1402.05167) Full Text: DOI arXiv
Bespalov, E. A.; Krotov, D. S. MDS codes in Doob graphs. (English. Russian original) Zbl 1437.94094 Probl. Inf. Transm. 53, No. 2, 136-154 (2017); translation from Probl. Peredachi Inf. 53, No. 2, 40-59 (2017). MSC: 94B25 05C15 05C90 PDFBibTeX XMLCite \textit{E. A. Bespalov} and \textit{D. S. Krotov}, Probl. Inf. Transm. 53, No. 2, 136--154 (2017; Zbl 1437.94094); translation from Probl. Peredachi Inf. 53, No. 2, 40--59 (2017) Full Text: DOI arXiv
Krotov, Denis S. The minimum volume of subspace trades. (English) Zbl 1370.05035 Discrete Math. 340, No. 12, 2723-2731 (2017). MSC: 05B99 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 340, No. 12, 2723--2731 (2017; Zbl 1370.05035) Full Text: DOI arXiv
Krotov, Denis S. The extended 1-perfect trades in small hypercubes. (English) Zbl 1386.94109 Discrete Math. 340, No. 10, 2559-2572 (2017). MSC: 94B25 05B07 05B30 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 340, No. 10, 2559--2572 (2017; Zbl 1386.94109) Full Text: DOI arXiv
Krotov, Denis S. On the automorphism groups of the \(\mathbb Z_2\mathbb Z_4\)-linear 1-perfect and Preparata-like codes. (English) Zbl 1379.94063 Des. Codes Cryptography 83, No. 1, 169-177 (2017). MSC: 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov}, Des. Codes Cryptography 83, No. 1, 169--177 (2017; Zbl 1379.94063) Full Text: DOI arXiv
Krotov, Denis S.; Östergård, Patric R. J.; Pottonen, Olli Non-existence of a ternary constant weight \((16,5,15;2048)\) diameter perfect code. (English) Zbl 1348.94083 Adv. Math. Commun. 10, No. 2, 393-399 (2016). MSC: 94B05 PDFBibTeX XMLCite \textit{D. S. Krotov} et al., Adv. Math. Commun. 10, No. 2, 393--399 (2016; Zbl 1348.94083) Full Text: DOI arXiv
Bespalov, E. A.; Krotov, D. S. On one test for the switching separability of graphs modulo \(q\). (English. Russian original) Zbl 1338.05211 Sib. Math. J. 57, No. 1, 7-17 (2016); translation from Sib. Mat. Zh. 57, No. 1, 10-24 (2016). MSC: 05C70 05C22 05C25 PDFBibTeX XMLCite \textit{E. A. Bespalov} and \textit{D. S. Krotov}, Sib. Math. J. 57, No. 1, 7--17 (2016; Zbl 1338.05211); translation from Sib. Mat. Zh. 57, No. 1, 10--24 (2016) Full Text: DOI arXiv
Krotov, Denis S.; Potapov, Vladimir N. Constructions of transitive Latin hypercubeatin hypercubes. (English) Zbl 1331.05045 Eur. J. Comb. 54, 51-64 (2016). MSC: 05B15 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{V. N. Potapov}, Eur. J. Comb. 54, 51--64 (2016; Zbl 1331.05045) Full Text: DOI arXiv
Krotov, D. S.; Mogilnykh, I. Yu.; Potapov, V. N. To the theory of \(q\)-ary Steiner and other-type trades. (English) Zbl 1328.05025 Discrete Math. 339, No. 3, 1150-1157 (2016). MSC: 05B07 PDFBibTeX XMLCite \textit{D. S. Krotov} et al., Discrete Math. 339, No. 3, 1150--1157 (2016; Zbl 1328.05025) Full Text: DOI arXiv
Krotov, Denis S.; Villanueva, Mercè On the automorphism groups of the \(\mathbb Z_2\mathbb Z_4\)-linear Hadamard codes and their classification. (English) Zbl 1398.94219 Pinto, Raquel (ed.) et al., Coding theory and applications. 4th international castle meeting, ICMCTA, Palmela Castle, Portugal, September 15–18, 2014. Cham: Springer (ISBN 978-3-319-17295-8/hbk; 978-3-319-17296-5/ebook). CIM Series in Mathematical Sciences 3, 237-243 (2015). MSC: 94B05 11T71 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{M. Villanueva}, CIM Ser. Math. Sci 3, 237--243 (2015; Zbl 1398.94219) Full Text: DOI
Krotov, Denis S.; Sotnikova, Ev V. Embedding in \(q\)-ary 1-perfect codes and partitions. (English) Zbl 1372.94474 Discrete Math. 338, No. 11, 1856-1859 (2015). MSC: 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{E. V. Sotnikova}, Discrete Math. 338, No. 11, 1856--1859 (2015; Zbl 1372.94474) Full Text: DOI arXiv
Vorob’ev, K. V.; Krotov, D. S. Bounds for the size of a minimal 1-perfect bitrade in a Hamming graph. (Russian, English) Zbl 1324.05047 Diskretn. Anal. Issled. Oper. 21, No. 6, 3-10 (2014); translation in J. Appl. Ind. Math. 9, No. 1, 141-146 (2015). MSC: 05C12 PDFBibTeX XMLCite \textit{K. V. Vorob'ev} and \textit{D. S. Krotov}, Diskretn. Anal. Issled. Oper. 21, No. 6, 3--10 (2014; Zbl 1324.05047); translation in J. Appl. Ind. Math. 9, No. 1, 141--146 (2015) Full Text: DOI
Krotov, Denis S. On calculation of the interweight distribution of an equitable partition. (English) Zbl 1303.05156 J. Algebr. Comb. 40, No. 2, 373-386 (2014). MSC: 05C70 05C65 05C15 05C31 PDFBibTeX XMLCite \textit{D. S. Krotov}, J. Algebr. Comb. 40, No. 2, 373--386 (2014; Zbl 1303.05156) Full Text: DOI arXiv
Krotov, Denis S. On the binary codes with parameters of triply-shortened 1-perfect codes. (English) Zbl 1272.94094 Des. Codes Cryptography 64, No. 3, 275-283 (2012). Reviewer: Jon-Lark Kim (Seoul) MSC: 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov}, Des. Codes Cryptography 64, No. 3, 275--283 (2012; Zbl 1272.94094) Full Text: DOI arXiv
Krotov, Denis S. On weight distributions of perfect colorings and completely regular codes. (English) Zbl 1235.94065 Des. Codes Cryptography 61, No. 3, 315-329 (2011). MSC: 94B25 05B30 05C12 05C15 PDFBibTeX XMLCite \textit{D. S. Krotov}, Des. Codes Cryptography 61, No. 3, 315--329 (2011; Zbl 1235.94065) Full Text: DOI arXiv
Krotov, Denis S.; Potapov, Vladimir N. On connection between reducibility of an \(n\)-ary quasigroup and that of its retracts. (English) Zbl 1205.20067 Discrete Math. 311, No. 1, 58-66 (2011). MSC: 20N15 05B15 20N05 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{V. N. Potapov}, Discrete Math. 311, No. 1, 58--66 (2011; Zbl 1205.20067) Full Text: DOI arXiv
Krotov, D. S.; Potapov, V. N. On switching equivalence of \(n\)-ary quasigroups of order 4 and perfect binary codes. (English. Russian original) Zbl 1241.94035 Probl. Inf. Transm. 46, No. 3, 219-224 (2010); translation from Probl. Peredachi Inf. 46, No. 3, 22-28 (2010). MSC: 94B25 20N15 PDFBibTeX XMLCite \textit{D. S. Krotov} and \textit{V. N. Potapov}, Probl. Inf. Transm. 46, No. 3, 219--224 (2010; Zbl 1241.94035); translation from Probl. Peredachi Inf. 46, No. 3, 22--28 (2010) Full Text: DOI
Krotov, Denis S. On the binary codes with parameters of doubly-shortened 1-perfect codes. (English) Zbl 1201.94131 Des. Codes Cryptography 57, No. 2, 181-194 (2010). Reviewer: Bal Kishan Dass (Delhi) MSC: 94B25 94B60 PDFBibTeX XMLCite \textit{D. S. Krotov}, Des. Codes Cryptography 57, No. 2, 181--194 (2010; Zbl 1201.94131) Full Text: DOI arXiv
Avgustinovich, Sergey V.; Krotov, Denis S. Embedding in a perfect code. (English) Zbl 1197.94226 J. Comb. Des. 17, No. 5, 419-423 (2009). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 94B25 11T71 PDFBibTeX XMLCite \textit{S. V. Avgustinovich} and \textit{D. S. Krotov}, J. Comb. Des. 17, No. 5, 419--423 (2009; Zbl 1197.94226) Full Text: DOI arXiv
Krotov, Denis S. On reducibility of \(n\)-ary quasigroups. (English) Zbl 1190.05039 Discrete Math. 308, No. 22, 5289-5297 (2008). MSC: 05B99 20N15 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 308, No. 22, 5289--5297 (2008; Zbl 1190.05039) Full Text: DOI arXiv
Krotov, Denis S. On decomposability of 4-ary distance 2 MDS codes, double-codes, and \(n\)-quasigroups of order 4. (English) Zbl 1151.05012 Discrete Math. 308, No. 15, 3322-3334 (2008). Reviewer: Bal Kishan Dass (Delhi) MSC: 05B99 20N15 94B25 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 308, No. 15, 3322--3334 (2008; Zbl 1151.05012) Full Text: DOI arXiv
Krotov, D. S. On diameter perfect constant-weight ternary codes. (English) Zbl 1143.94021 Discrete Math. 308, No. 14, 3104-3114 (2008). MSC: 94B25 05C70 PDFBibTeX XMLCite \textit{D. S. Krotov}, Discrete Math. 308, No. 14, 3104--3114 (2008; Zbl 1143.94021) Full Text: DOI arXiv
Krotov, Denis On irreducible \(n\)-ary quasigroups with reducible retracts. (English) Zbl 1141.20046 Eur. J. Comb. 29, No. 2, 507-513 (2008). Reviewer: G. I. Zhitomirskij (Herzliyya) MSC: 20N15 20N05 06E30 PDFBibTeX XMLCite \textit{D. Krotov}, Eur. J. Comb. 29, No. 2, 507--513 (2008; Zbl 1141.20046) Full Text: DOI arXiv