Self-orthogonal and quantum codes over chain rings

Maryam Bajalan; Mina Moeini; Bahattin Yildiz

doi:10.13069/jacodesmath.v11i2.304

Self-orthogonal and quantum codes over chain rings

Maryam Bajalan, Mina Moeini, Bahattin Yildiz

Research output: Contribution to journal › Article › peer-review

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 F_q. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasitwisted 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.

Original language	English (US)
Pages (from-to)	139-150
Number of pages	12
Journal	Journal of Algebra Combinatorics Discrete Structures and Applications
Volume	11
Issue number	2
DOIs	https://doi.org/10.13069/jacodesmath.v11i2.304
State	Published - May 21 2024
Externally published	Yes

Keywords

Gray map
Griesmer code
Quantum code
Quasi-twisted code
Self-orthogonal code

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.13069/jacodesmath.v11i2.304

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AU - Yildiz, Bahattin

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N2 - 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 Fq. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasitwisted 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.

AB - 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 Fq. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasitwisted 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.

KW - Gray map

KW - Griesmer code

KW - Quantum code

KW - Quasi-twisted code

KW - Self-orthogonal code

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JF - Journal of Algebra Combinatorics Discrete Structures and Applications

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Self-orthogonal and quantum codes over chain rings

Abstract

Keywords

ASJC Scopus subject areas

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