On self-dual and LCD double circulant codes over Fq+uFq+vFq+uvFq

Double circulant codes of length 2n over a non-chain ring Fq+uFq+vFq+uvFq, u2=v2=0, uv=vu, were studied when q was a prime power. Exact enumerations of self-dual and LCD double circulant codes for a positive integer n were given. Using a distance-preserving Gray map, self-dual and LCD codes of length 8n over Fq were constructed when q was even. Using random coding and the Artin conjecture, the modified Varshamov-Gilbert bounds were derived on the relative distance of the codes considered, building on exact enumeration results for given n and q.