Mixed skew cyclic codes over rings

Abstract

This paper explores different types of skew cyclic codes by generating special subclasses with additional desirable properties. Specifically, we are interested in skew cyclic codes over mixed rings. We study some algebraic and structural properties of these codes and their constructions. We study skew cyclic codes over the mixed alphabet ring $\mathbb{F}_q(\mathbb{F}_q+v\mathbb{F}_q)$ under a mixed automorphism $(\theta,\tilde{\theta})$ and we give the structure of these codes for an arbitrary length via the non-commutative ring $\mathbb{F}_q[x,\theta](\mathbb{F}_q+v\mathbb{F}_q)[x,\tilde{\theta}]$. A condition for the existence of linear complementary dual (LCD) codes (which play an important role in practical applications such as armoring implementations against side-channel attacks and fault injection attacks) are explored specifically for skew cyclic codes.

Received: 5 July 2024 | Accepted: 13 October 2024