We investigate a $H$-invariant linear code $C$ over the finite field $F_{p}$ where $H$ is a group of linear transformations. We show that if $H$ is a noncyclic abelian group and $(\vert {H}\vert ,p)=1$, then the code $C$ is the sum of the centralizer codes $C_{c}(h)$ where $h$ is a nonidentity element of $H$. Moreover if $A$ is subgroup of $H$ such that $A\cong Z_{q} \times Z_{q}$, $q\ne p$, then dim $C$ is known when the dimension of $C_{c}(K)$ is known for each subgroup $K\ne 1$ of $A$. In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine codes and their centralizers. New results concerning the dimensions of these codes and their centralizers are obtained.
@article{107932,
author = {Partha Pratim Dey},
title = {Exploring invariant linear codes through generators and centralizers},
journal = {Archivum Mathematicum},
volume = {041},
year = {2005},
pages = {17-26},
zbl = {1115.05097},
mrnumber = {2142140},
language = {en},
url = {http://dml.mathdoc.fr/item/107932}
}
Dey, Partha Pratim. Exploring invariant linear codes through generators and centralizers. Archivum Mathematicum, Tome 041 (2005) pp. 17-26. http://gdmltest.u-ga.fr/item/107932/
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