  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).
