Basic Reed–Muller codes and their connections with powers of radical of group algebra over a non-prime field
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 46-49
Cet article a éte moissonné depuis la source Math-Net.Ru
We show that there are no equalities between basic Reed–Muller codes and radical powers of a corresponding group algebra over non-prime field.
@article{VMUMM_2013_6_a8,
author = {I. N. Tumaikin},
title = {Basic {Reed{\textendash}Muller} codes and their connections with powers of radical of group algebra over a non-prime field},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {46--49},
year = {2013},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a8/}
}
TY - JOUR AU - I. N. Tumaikin TI - Basic Reed–Muller codes and their connections with powers of radical of group algebra over a non-prime field JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2013 SP - 46 EP - 49 IS - 6 UR - http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a8/ LA - ru ID - VMUMM_2013_6_a8 ER -
%0 Journal Article %A I. N. Tumaikin %T Basic Reed–Muller codes and their connections with powers of radical of group algebra over a non-prime field %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2013 %P 46-49 %N 6 %U http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a8/ %G ru %F VMUMM_2013_6_a8
I. N. Tumaikin. Basic Reed–Muller codes and their connections with powers of radical of group algebra over a non-prime field. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 46-49. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a8/
[1] Berman S.D., “O teorii gruppovykh kodov”, Kibernetika, 3 (1967), 31–39
[2] Kouselo E., Gonsales S., Markov V.T., Martines K., Nechaev A.A., “Predstavleniya kodov Rida–Solomona i Rida–Mallera idealami”, Algebra i logika, 51:3 (2012), 297–320 | MR
[3] Landrock P., Manz O., “Classical codes as ideals in group algebras”, Designs, codes and cryptography, 2:3 (1992), 273–285 | DOI | MR
[4] Assmus E.F. Jr., Key J.D., “Polynomial codes and finite geometries”, Handbook of coding theory, v. 2, Elsevier, Amsterdam, 1998, 1269–1343 | MR
[5] Jennings S.A., “The structure of the group ring of a p-group over a modular field”, Trans. Amer. Math. Soc., 50 (1941), 175–185 | MR