On self dual double circulant codes
Self dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta dihedral in odd characteristic. Exact counting formulae are derived for them, generalizing some old results of MacWilliams on the enumeration of circulant orthogonal matrices. These formulae, in turn, are instrumental in deriving a Varshamov Gilbert bound on the relative minimum distance of this family of codes.
Des. Codes Cryptogr.