Self-orthogonal and quantum codes over chain rings

Maryam Bajelan; Mina  Moeini; Bahattin  Yildiz

doi:10.13069/jacodesmath.v11i2.304

Maryam Bajelan
Mina Moeini Department of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran
Bahattin Yildiz Intel Labs, Santa Clara, CA 95035, USA

DOI: https://doi.org/10.13069/jacodesmath.v11i2.304

Keywords: Gray map, Self-orthogonal code, Quantum code, Quasi-twisted code, Griesmer code

Abstract

In this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field $\mathbb{F}_q$. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes.