\(k\)-configurations. (English. Russian original) Zbl 1487.15040
Proc. Steklov Inst. Math. 316, 233-253 (2022); translation from Tr. Mat. Inst. Steklova 316, 248-269 (2022).
Summary: We survey the results of many authors on the construction of nonsingular binary matrices with the same number of ones in their rows and columns and in the rows and columns of their inverses.
MSC:
| 15B36 | Matrices of integers |
| 15B34 | Boolean and Hadamard matrices |
| 05B05 | Combinatorial aspects of block designs |
| 51E05 | General block designs in finite geometry |
| 51M20 | Polyhedra and polytopes; regular figures, division of spaces |
Keywords:
configurations; block designs; finite groups; symmetric graphs; regular polyhedra; surface triangulationsReferences:
| [1] | Cameron, P. J.; Lint, J. H. Van, Graph Theory, Coding Theory and Block Designs (1975), Cambridge: Cambridge Univ. Press, Cambridge · Zbl 0314.94008 · doi:10.1017/CBO9781107325425 |
| [2] | Cormen, T. H.; Leiserson, C. E.; Rivest, R. L., Introduction to Algorithms (1990), Cambridge, MA: MIT Press, Cambridge, MA · Zbl 1158.68538 |
| [3] | Daemen, J.; Knudsen, L.; Rijmen, V., The block cipher Square, Fast Software Encryption: Proc. 4th Int. Workshop FSE’97, Haifa, 1997, 149-165 (1997), Berlin: Springer, Berlin · Zbl 1385.94025 · doi:10.1007/BFb0052343 |
| [4] | Daemen, J.; Rijmen, V., The Design of Rijndael: AES—The Advanced Encryption Standard (2002), Berlin: Springer, Berlin · Zbl 1065.94005 · doi:10.1007/978-3-662-04722-4 |
| [5] | Frolov, A. A., Classification of indecomposable Abelian \((v,5)\)-groups, Discrete Math. Appl., 18, 1, 99-114 (2008) · Zbl 1173.05309 · doi:10.1515/DMA.2008.008 |
| [6] | Grigor’ev, N. A., Regular simplices inscribed in a cube and Hadamard matrices, Proc. Steklov Inst. Math., 152, 97-98 (1982) · Zbl 0502.52009 |
| [7] | Hall Jr., M., Combinatorial Theory (1967), Waltham, MA: Blaisdell Publ., Waltham, MA · Zbl 0196.02401 |
| [8] | Harary, F., Graph Theory (1969), Reading, MA: Addison-Wesley, Reading, MA · Zbl 0182.57702 · doi:10.21236/AD0705364 |
| [9] | Kárteszi, F., Introduction to Finite Geometries (1976), Budapest: Akad. Kiado, Budapest · Zbl 0325.50001 |
| [10] | Kwon, D., New block cipher: ARIA, Information Security and Cryptology—ICISC 2003: Proc. 6th Int. Conf., Seoul, 2003, 432-445 (2004), Berlin: Springer, Berlin · Zbl 1092.94509 · doi:10.1007/978-3-540-24691-6_32 |
| [11] | Lidl, R.; Niederreiter, H., Finite Fields (1983), Reading, MA: Addison-Wesley, Reading, MA · Zbl 0554.12010 |
| [12] | Lim, C. H., A revisited version of Crypton: Crypton v1.0, Fast Software Encryption: Proc. 6th Int. Workshop FSE’99, Rome, 1999, 31-45 (1999), Berlin: Springer, Berlin · Zbl 0942.94002 · doi:10.1007/3-540-48519-8_3 |
| [13] | Malyshev, F. M., Three series of 5-configurations, Mat. Vopr. Kriptografii, 4, 3, 83-97 (2013) · Zbl 1475.05022 · doi:10.4213/mvk93 |
| [14] | Malyshev, F. M., Four infinite series of \(k\)-configurations, Mat. Vopr. Kriptografii, 4, 4, 65-75 (2013) · Zbl 1475.05023 · doi:10.4213/mvk100 |
| [15] | Malyshev, F. M.; Frolov, A. A., Classification of \((v,3)\)-configurations, Math. Notes, 91, 5-6, 689-696 (2012) · Zbl 1408.05027 · doi:10.1134/S0001434612050100 |
| [16] | Malyshev, F. M.; Tarakanov, V. E., On \((v,k)\)-configurations, Sb. Math., 192, 9, 1341-1364 (2001) · Zbl 1020.05017 · doi:10.1070/SM2001v192n09ABEH000595 |
| [17] | Panasenko, S. P., Encryption Algorithms: Special Handbook (2009), St. Petersburg: BKhV-Peterburg, St. Petersburg |
| [18] | Park, J. H., Security analysis of mCrypton proper to low-cost ubiquitous computing devices and applications, Int. J. Commun. Syst., 22, 8, 959-969 (2009) · doi:10.1002/dac.1008 |
| [19] | Moser, W. O. J., Problems in Discrete Geometry (1977), Montreal: McGill Univ., Montreal |
| [20] | Sachkov, V. N., Combinatorial Methods in Discrete Mathematics (1995), Cambridge: Cambridge Univ. Press, Cambridge · Zbl 0845.05003 |
| [21] | Sachkov, V. N.; Tarakanov, V. E., Combinatorics of Nonnegative Matrices (2002), Providence, RI: Am. Math. Soc., Providence, RI · Zbl 1006.05001 · doi:10.1090/mmono/213 |
| [22] | Tarakanov, V. E., Combinatorial Problems and \((0,1)\)-Matrices (1985), Moscow: Nauka, Moscow · Zbl 0641.05012 |
| [23] | Trishin, A. E., Examples of \((v,k)\)-matrices, Herald Inst. Complex Strategic Stud., Ser. K, Spec. Issue Dedicated to the Centenary of A. N. Kolmogorov’s Birth, 179-185 (2003), Moscow: Inst. Kriptografii Svyazi Inform. Akad. Fed. Sluzhby Bezop. Ross. Fed., Moscow |
| [24] | Trishin, A. E., Classification of circulant \((v,5)\)-matrices, Obozr. Prikl. Prom. Mat., 11, 2, 258-259 (2004) |
| [25] | Trishin, A. E.; Frolov, A. A., Method for constructing \((v,k)\)-matrices using the trace function, VII All-Russian Symposium on Applied and Industrial Mathematics: Abstracts, 362-364 (2006), Moscow: Obozr. Prikl. Prom. Mat., Moscow |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
