Dual codes of systematic group codes over abelian groups

Abstract

For systematic codes over finite fields the following result is well known: If [I¦P] is the generator matrix then the generator matrix of its dual code is [ −P^tr¦I]. The main result is a generalization of this for systematic group codes over finite abelian groups. It is shown that given the endomorphisms which characterize a group code over an abelian group, the endomorphisms which characterize its dual code are identified easily. The self-dual codes are also characterized. It is shown that there are self-dual and MDS group codes over elementary abelian groups which can not be obtained as linear codes over finite fields.