On Self-dual and LCD Double Circulant Codes over a Non-chain Ring

In this paper, we study double circulant codes of length 2n over the non-chain ring R=F_q + vF_q + v²F _q, where q is an odd prime power and v³=v. Exact enumerations of self-dual and LCD double circulant codes of length 2n over R are derived. When n is an odd prime, using random coding, we obtain families of asymptotically good self-dual and LCD codes of length 6n over F_q.