Geodesic
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 
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/
@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

Voir la notice de l'article provenant de 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.

[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