Construction of self-dual codes over finite rings

We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Z p m (or Z m ) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79–95] over large finite fields GF ( p m ) to finite rings Z p m (or Z m ). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Z p m or Z p q with q an odd prime, where p m = 25 , 125, 169, 289 and p q = 65 , 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes.