Self-dual codes over GF(7) and orthogonal designs

Abstract

Self-dual codes and orthogonal designs have been studied for a long time as separate research areas. In this paper we show a strong relationship between them and orthogonal designs. The structure of orthogonal designs is such as to allow us a much faster and more systematic search for self-dual codes over GF(7). We describe some of the known methods for constructing self-dual codes and we develop a new construction method which is based on the orthogonal designs. Applying our method we are able to construct some new self-dual codes over GF(7). In particular we constructed two [16, 8, 7] and a [24, 12, 9] self-dual codes with new weight enumerators.