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 F 5 [ u ] ∕ u 2 > and of lengths 2 , 3 , 4 over the chain ring F 7 [ u ] ∕ u 2 > .