Self-dual codes from circulant matrices

In this paper, two general methods for constructing self-dual codes are presented. These methods use circulant matrices in circulant or bordered circulant structures to construct the suitable generator matrices. The necessary and sufficient conditions, for the generated codes to be self-dual, are provided. Special cases of the proposed methods include the well known "Pure Double Circulant" construction and the "Bordered Double circulant" construction of self-dual codes. As an example, the methods were applied to search for self-dual codes in GF(5). Many new inequivalent self-dual codes with best known distance are found