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Double Circulant Self-dual Codes on Sextic Cyclotomy (2006.07768v1)
Published 14 Jun 2020 in cs.IT and math.IT
Abstract: This paper contributes to construct double circulant self-dual codes by sextic cyclotomy. Generator matrixes of a family of pure double circulant codes and a family of double circulant codes with boundary are formed from sextic cyclotomic classes. These codes are proved to be self-dual on certain conditions. Moreover, experiments show that some of them are optimal self-dual codes or best than ever codes over GF}(2) and GF}(4).