## m-adic residue codes over Fq[v]/(v^s -v) and their applications to quantum codes

Quantum Information & Computation, vol.22, no.5-6, pp.427-439, 2022 (Journal Indexed in SCI)

• Publication Type: Article / Article
• Volume: 22 Issue: 5-6
• Publication Date: 2022
• Doi Number: 10.26421/qic22.5-6-4
• Title of Journal : Quantum Information & Computation
• Page Numbers: pp.427-439

#### Abstract

In this paper, we investigate the algebraic structure of the non-local ring $\mathcal{R}_q=\mathbb{F}_q[v]/\langle v^{2}+1\rangle$ and we identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their dual over it. Furthermore, we give a necessary and sufficient conditions for the skew constacyclic codes over $\mathcal{R}_q$ to be linear complementary dual. Eventually, applying Hermitian linear complementary dual skew constacyclic codes over $\mathcal{R}_q$ and a Gray type map, we give a class of entanglement-assisted quantum codes with maximal entanglement.