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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 × Z q , q p , then dim  C is known when the dimension of C c ( K ) is known for each subgroup K 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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