$k$-Configurations

F. M. Malyshev

Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 248-269.

Résumé

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.

Détail

Mots-clés : configurations, surface triangulations.
Keywords: block designs, finite groups, symmetric graphs, regular polyhedra

Bibliographie

[1] P. J. Cameron and J. H. Van Lint, Graph Theory, Coding Theory and Block Designs, LMS Lect. Note Ser., 19, Cambridge Univ. Press, Cambridge, 1975 | MR | Zbl

[2] T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990 | MR | Zbl

[3] Daemen J., Knudsen L., Rijmen V., “The block cipher Square”, Fast software encryption: Proc. 4th Int. Workshop FSE'97 (Haifa, 1997), Lect. Notes Comput. Sci., 1267, Springer, Berlin, 1997, 149–165 | DOI | Zbl

[4] Daemen J., Rijmen V., The design of Rijndael: AES—the Advanced Encryption Standard, Springer, Berlin, 2002 | MR | Zbl

[5] A. A. Frolov, “Classification of indecomposable Abelian $(v,5)$-groups”, Discrete Math. Appl., 18:1 (2008), 99–114 | DOI | MR | Zbl

[6] N. A. Grigor'ev, “Regular simplices inscribed in a cube and Hadamard matrices”, Proc. Steklov Inst. Math., 152 (1982), 97–98

[7] M. Hall Jr., Combinatorial Theory, Blaisdell Publ., Waltham, MA, 1967 | MR | MR | Zbl

[8] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969 | MR | Zbl

[9] F. Kárteszi, Introduction to Finite Geometries, Akad. Kiado, Budapest, 1976 | MR | Zbl

[10] Kwon D. et al., “New block cipher: ARIA”, Information security and cryptology—ICISC 2003, Proc. 6th Int. Conf. (Seoul, 2003), Lect. Notes Comput. Sci., 2971, Springer, Berlin, 2004, 432–445 | DOI | MR | Zbl

[11] R. Lidl and H. Niederreiter, Finite Fields, Encycl. Math. Appl., 20, Addison-Wesley, Reading, MA, 1983 | MR | MR | Zbl

[12] Lim C.H., “A revisited version of Crypton: Crypton v1.0”, Fast software encryption, Proc. 6th Int. Workshop FSE'99 (Rome, 1999), Lect. Notes Comput. Sci., 1636, Springer, Berlin, 1999, 31–45 | DOI | MR | Zbl

[13] F. M. Malyshev, “Three series of 5-configurations”, Mat. Vopr. Kriptografii, 4:3 (2013), 83–97 | DOI | Zbl

[14] Malyshev F.M., “Chetyre beskonechnye serii $k$-konfiguratsii”, Mat. vopr. kriptogr., 4:4 (2013), 65–75 | Zbl

[15] F. M. Malyshev and A. A. Frolov, “Classification of $(v,3)$-configurations”, Math. Notes, 91:5–6 (2012), 689–696 | DOI | MR | Zbl

[16] F. M. Malyshev and V. E. Tarakanov, “On $(v,k)$-configurations”, Sb. Math., 192:9 (2001), 1341–1364 | DOI | MR | Zbl

[17] Panasenko S.P., Algoritmy shifrovaniya: Spetsialnyi spravochnik, BKhV-Peterburg, SPb., 2009

[18] Park J.H., “Security analysis of mCrypton proper to low-cost ubiquitous computing devices and applications”, Int. J. Commun. Syst., 22:8 (2009), 959–969 | DOI

[19] Problems in discrete geometry, presented at the Discrete Geometry Week (Oberwolfach, 1977), ed. by W.O.J. Moser, McGill Univ., Montreal, 1977

[20] V. N. Sachkov, Combinatorial Methods in Discrete Mathematics, Encycl. Math. Appl., 55, Cambridge Univ. Press, Cambridge, 1995 | MR | MR | Zbl

[21] V. N. Sachkov and V. E. Tarakanov, Combinatorics of Nonnegative Matrices, Transl. Math. Monogr., 213, Am. Math. Soc., Providence, RI, 2002 | DOI | MR | MR | Zbl

[22] Tarakanov V.E., Kombinatornye zadachi i $(0,1)$-matritsy, Nauka, M., 1985 | MR

[23] Trishin A.E., “Primery $(v,k)$-matrits”, Vestn. IKSI. Ser. K, Spets. vyp., posv. 100-letiyu ak. A.N. Kolmogorova, In-t kriptogr., svyazi i informatiki Akad. FSB RF, M., 2003, 179–185

[24] Trishin A.E., “Klassifikatsiya tsirkulyantnykh $(v,5)$-matrits”, Obozr. prikl. i promyshl. matematiki, 11:2 (2004), 258–259 | MR

[25] Trishin A.E., Frolov A.A., “Sposob postroeniya $(v,k)$-matrits pri pomoschi funktsii sled”, VII Vserossiiskii simpozium po prikladnoi i promyshlennoi matematike, Tez. dokl., Obozr. prikl. i promyshl. matematiki, M., 2006, 362–364