Self-dual Codes over Small Prime Fields from Combinatorial Designs

Abstract

In this paper, we give some new extremal ternary self-dual codes which are constructed by skew-Hadamard matrices. This has been achieved with the aid of a recently presented modification of a known construction method. In addition, we survey the known results for self-dual codes over GF (5) constructed via combinatorial designs, i.e. Hadamard and skew-Hadamard matrices, and we give a new self-dual code of length 72 and dimension 36 whose minimum weight is 16 over GF (5) for the first time. Furthermore, we give some properties of the generated self-dual codes interpreted in terms of algebraic coding theory, such as the orders of their automorphism groups and the corresponding weight enumerators.