Address.
Department of Computer Science and Engineering,
North South University, Dhaka, Bangladesh
E-mail. ppd@northsouth.edu
Abstract.
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 $A\cong Z_{q}
\times
Z_{q}$, $q\neq p$, then $\dim C$ is known when the dimension of $C_{c}(K)$ is
known for each subgroup $K\neq 1$ 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.
AMSclassification. 05E20.
Keywords. Invariant code, centralizer, affine plan.