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Exploring invariant linear codes through generators and centralizers

Partha Pratim Dey — 2005

Archivum Mathematicum

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 $(| H |, p) = 1$ , 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 $A ≅ Z_{q} \times Z_{q}$ , $q \neq p$ , 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...

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