On self-dual and LCD quasi-twisted codes of index two over a special chain ring

International audienceLet q be a prime power, and let F q denote the finite field of order q. Consider the chain ring R k = F q [u]/ u k with k ≥ 1 an integer. We study self-dual and LCD quasi-twisted codes of index two and twisting constant λ over R k for the metric induced by the standard Gray map. Some special factorizations of x m − λ over R k are studied. By random coding, we obtain four classes of asymptotically good self-dual λ-circulant codes and four classes of asymptotically good LCD λ-circulant codes over R k