LAUSR

Let q be a prime power, and let ????q$\mathbb {F}_{q}$ denote the finite field of order q. Consider the chain ring Rk=????q[u]/〈uk〉$R_{k}=\mathbb {F}_{q}[u]/\langle u^{k}\rangle $ with k ≥ 1 an integer. We study self-dual and LCD quasi-twisted codes of index two and twisting constant λ over Rk for the metric induced by the standard Gray map. Some special factorizations of xm − λ over Rk 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 Rk.