On self-dual and LCD double circulant and double negacirculant codes over F_q + uF_q
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Double circulant codes of length 2n over the semilocal ring R = F_q + uF_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 2n 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 2n is given. Employing a duality-preserving Gray map, self-dual and LCD codes of length 4n over F_q are constructed. Using random coding and the Artin conjecture, the relative distance of these codes is bounded below. The parameters of examples of the modest length are computed. Several such codes are optimal.
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