Self-orthogonal and quantum codes over chain rings

Authors

  • Maryam Bajelan Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113, Sofia, Bulgaria https://orcid.org/0000-0003-3828-825X
  • Mina Moeini Department of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran
  • Bahattin Yildiz Director of Security Research, LG Electronics, Santa Clara, CA 95054, USA https://orcid.org/0000-0001-8106-3123

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.

Received: 19 September 2023 | Accepted: 18 January 2024

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Published

2024-05-06

How to Cite

Bajelan, M., Moeini, M. ., & Yildiz, B. . (2024). Self-orthogonal and quantum codes over chain rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 11(2), 139–150. https://doi.org/10.13069/jacodesmath.v11i2.304

Issue

Vol. 11 Issue 2: May 2024

Section

Articles