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@article{PDM_2012_4_a2, author = {V. T. Markov and A. V. Mikhalev and A. V. Gribov and P. A. Zolotykh and S. S. Skazhenik}, title = {Quasigroups and rings in coding theory and cryptography}, journal = {Prikladna\^a diskretna\^a matematika}, pages = {31--52}, publisher = {mathdoc}, number = {4}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/PDM_2012_4_a2/} }
TY - JOUR AU - V. T. Markov AU - A. V. Mikhalev AU - A. V. Gribov AU - P. A. Zolotykh AU - S. S. Skazhenik TI - Quasigroups and rings in coding theory and cryptography JO - Prikladnaâ diskretnaâ matematika PY - 2012 SP - 31 EP - 52 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PDM_2012_4_a2/ LA - ru ID - PDM_2012_4_a2 ER -
%0 Journal Article %A V. T. Markov %A A. V. Mikhalev %A A. V. Gribov %A P. A. Zolotykh %A S. S. Skazhenik %T Quasigroups and rings in coding theory and cryptography %J Prikladnaâ diskretnaâ matematika %D 2012 %P 31-52 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/PDM_2012_4_a2/ %G ru %F PDM_2012_4_a2
V. T. Markov; A. V. Mikhalev; A. V. Gribov; P. A. Zolotykh; S. S. Skazhenik. Quasigroups and rings in coding theory and cryptography. Prikladnaâ diskretnaâ matematika, no. 4 (2012), pp. 31-52. http://geodesic.mathdoc.fr/item/PDM_2012_4_a2/
[1] Rososhek S. K., “Kriptosistemy gruppovykh kolets”, Vestnik Tomskogo gosuniversiteta. Prilozhenie, 2003, no. 6, 57–62
[2] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967, 223 pp. | MR | Zbl
[3] Pflugfelder H. O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990 | MR
[4] Smith J. D. H., An Introduction to Quasigroups and their Representations, Chapman Hall/CRC, Boca Raton, 2007 | MR | Zbl
[5] Vojtechovsky P., “Generators for finite simple Moufang loops”, J. Group Theory, 6 (2003), 169–174 | MR | Zbl
[6] Paige L. J., “A class of simple Moufang loops”, Proc. Amer. Math. Soc., 7:3 (1956), 471–482 | DOI | MR | Zbl
[7] Vojtechovsky P., Finite simple Moufang loops, PhD thesis, Department of Mathematics, Iowa State University, Ames, 2001
[8] Conrad P., “Generalized semigroup rings”, J. Indian Math. Soc., 21 (1957), 73–95 | MR
[9] Gribov A. V., Zolotykh P. A., Mikhalëv A. V., “Postroenie algebraicheskoi kriptosistemy nad kvazigruppovym koltsom”, Matematicheskie voprosy kriptografii, 1:4 (2010), 23–32
[10] Kuzucuoglu F., Levchuk V. M., “The automorphism group of certain radical matrix rings”, J. Algebra, 243:2 (2001), 473–485 | DOI | MR | Zbl
[11] Magliveras S. S., Stinson D. R., Tran van Trung, “New approaches to designing public key cryptosystem using one-way functions and trap-doors in finite groups”, J. Cryptology, 15:4 (2008), 285–297 | DOI | MR
[12] MakVillyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979
[13] Heise W., Quattrocci P., Informations und Codierungstheorie, Springer, Berlin–Heidelberg, 1995 | MR | Zbl
[14] Gonsales S., Kouselo E., Markov V. T., Nechaev A. A., “Rekursivnye MDR-kody i rekursivno differentsiruemye kvazigruppy”, Diskretnaya matematika, 10:2 (1998), 3–29 | DOI | MR | Zbl
[15] Gonsales S., Kouselo E., Markov V. T., Nechaev A. A., “Gruppovye kody i ikh neassotsiativnye obobscheniya”, Diskretnaya matematika, 16:1 (2004), 146–156 | DOI | MR | Zbl
[16] Brouwer A. E., “Bounds on linear codes”, Handbook of Coding Theory, Elsevier, Amsterdam, 1998, 295–461 | MR | Zbl
[17] Grassl M., “Searching for linear codes with large minimum distance”, Discovering Mathematics with Magma, 19, Springer, Berlin–Heidelberg, 2006, 287–313 | DOI | MR | Zbl
[18] Couselo E., Gonzalez S., Markov V., et al., “Some constructions of linearly optimal group codes”, Linear Algebra and its Applications, 433 (2010), 356–364 | DOI | MR | Zbl
[19] Charpin P., “Les codes ve Reed–Solomon en tant qu'idéaux d'une algèbre modulaire”, C. R. Acad. Sci. Paris, 294:17 (1982), 597–600 (French, English summary) | MR | Zbl
[20] Landrock P., Manz O., “Classical codes as ideals in group algebras”, Designs, Codes and Cryptography, 2 (1992), 273–285 | DOI | MR | Zbl