Mass formulae for Euclidean self-orthogonal and self-dual codes over finite commutative chain rings

Abstract

In this paper, we obtain explicit mass formulae for all Euclidean self-orthogonal and self-dual codes of an arbitrary length over finite commutative chain rings of odd characteristic. With the help of these mass formulae, we classify all Euclidean self-orthogonal and self-dual codes of lengths 2,3,4,5 over the chain ring F5[u]∕<u2> and of lengths 2,3,4 over the chain ring F7[u]∕<u2>.