The classification of self-dual modular codes

Abstract

A classification method of self-dual codes over Z m is given. If m = r s with relatively prime integers r and s, then the classification can be accomplished by double coset decompositions of S n by automorphism groups of self-dual codes over Z r and Z s . We classify self-dual codes of length 4 over Z p for all primes p in terms of their automorphism groups and then apply our method to classify self-dual codes over Z m for arbitrary integer m. Self-dual codes of length 8 are also classified over Z p q for p , q = 2 , 3 , 5 , 7 .