On self-dual and LCD double circulant and double negacirculant codes over Fq+uFq

Double circulant codes of length 2 n over the non-local ring R = F q + u F q , u 2 = u , are studied when q is an odd prime power, and − 1 is a square in F q . Double negacirculant codes of length 2 n are studied over R when n is even, and q is an odd prime power. Exact enumeration of self-dual and LCD such codes for given length 2 n is given. Employing a duality-preserving Gray map, self-dual and LCD codes of length 4 n over F q are constructed. Using random coding and the Artin conjecture, the relative distance of these codes is bounded below for n → ∞ . The parameters of examples of modest lengths are computed. Several such codes are optimal.