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

Minjia Shi (1) , Liqin Qian , Patrick Sole (2)

1 Anhui University [Hefei]
2 I2M - Institut de Mathématiques de Marseille

Let 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 .

Domaines: Informatique [cs]

Minjia Shi, Liqin Qian, Patrick Sole. On self-dual and LCD quasi-twisted codes of index two over a special chain ring. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2019, 11, pp.717 - 734. ⟨10.1007/s12095-018-0322-5⟩. ⟨hal-02411619⟩