Abstract:
We suggest a method of construction of orthogonal quasigroups systems and orthogonal Latin squares by means of Frobenius groups. It is proved that this method generalizes many (but not all) existing methods of orthogonal Latin squares construction by means of groups.
Key words:
quasigroup, Latin square, system of orthogonal quasigroups, orthogonal Latin squares, regular set of permutations, regular automorphism of a group.
Received 23.VI.2010
Document Type:
Article
UDC:512.548.7
Language: Russian
Citation:
M. M. Gluhov, “On a method of construction of orthogonal quasigroup systems by means of groups”, Mat. Vopr. Kriptogr., 2:4 (2011), 5–24
\Bibitem{Glu11}
\by M.~M.~Gluhov
\paper On a method of construction of orthogonal quasigroup systems by means of groups
\jour Mat. Vopr. Kriptogr.
\yr 2011
\vol 2
\issue 4
\pages 5--24
\mathnet{http://mi.mathnet.ru/mvk40}
\crossref{https://doi.org/10.4213/mvk40}
Linking options:
https://www.mathnet.ru/eng/mvk40
https://doi.org/10.4213/mvk40
https://www.mathnet.ru/eng/mvk/v2/i4/p5
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A. Yu. Zubov, “Kriptosistema blochnogo gammirovaniya s autentifikatsiei”, Matem. vopr. kriptogr., 13:4 (2022), 5–35
A. V. Menyachikhin, “The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups”, Discrete Math. Appl., 31:5 (2021), 327–343
B. A. Pogorelov, M. A. Pudovkina, “Variatsii ortomorfizmov i psevdoadamarovykh preobrazovanii na neabelevoi gruppe”, PDM. Prilozhenie, 2019, no. 12, 24–27
S. V. Polin, “Families of quasigroup operations satisfying the generalized distributive law”, Discrete Math. Appl., 30:3 (2020), 187–202
A. V. Menyachikhin, “Orthomorphisms of Abelian groups with minimum possible pairwise distances”, Discrete Math. Appl., 30:3 (2020), 177–186
Denisov V O., “Criteria For Markov Block Ciphers”, Prikl. Diskretn. Mat., 2018, no. 41, 28–37
A. V. Menyachikhin, “Spectral-linear and spectral-differential methods for generating S-boxes having almost optimal cryptographic parameters”, Matem. vopr. kriptogr., 8:2 (2017), 97–116
S. V. Polin, “Elementary transformations of systems of equations over quasigroups and generalized identities”, Discrete Math. Appl., 29:6 (2019), 383–399
S. V. Polin, “Perestanovochnye reshetki otnoshenii ekvivalentnosti na dekartovykh proizvedeniyakh i soglasovannye s nimi sistemy uravnenii. II”, Matem. vopr. kriptogr., 8:3 (2017), 85–108
M. M. Glukhov, “O priblizhenii diskretnykh funktsii lineinymi funktsiyami”, Matem. vopr. kriptogr., 7:4 (2016), 29–50
S. V. Polin, “Perestanovochnye reshetki otnoshenii ekvivalentnosti na dekartovykh proizvedeniyakh i soglasovannye s nimi sistemy uravnenii. I”, Matem. vopr. kriptogr., 6:1 (2015), 135–158
A. E. Trishin, “O pokazatele nelineinosti kusochno-lineinykh podstanovok additivnoi gruppy polya $\mathbb F_{2^n}$”, PDM, 2015, no. 4(30), 32–42
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