On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings-Reference-Cited by-同舟云学术

On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

Published:2023-04-10 Issue:4 Volume:12 Page:367
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Ali Shakir¹^ORCID,Alali Amal S.²^ORCID,Jeelani Mohammad³^ORCID,Kurulay Muhammet⁴^ORCID,Öztas Elif Segah⁵^ORCID,Sharma Pushpendra¹^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India

2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

3. Department of Computer Application, Faculty of Science, Integral University, Lucknow 226001, India

4. Department of Mathematics, Yildiz Technical University, Istanbul 34000, Turkey

5. Department of Mathematics, Karamanoglu Mehmetbey University, Karaman 70100, Turkey

Abstract

Let Fq be a field of order q, where q is a power of an odd prime p, and α and β are two non-zero elements of Fq. The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/⟨u12−α2,u22−β2,u1u2−u2u1⟩. We decompose the ring R by using orthogonal idempotents Δ1,Δ2,Δ3, and Δ4 as R=Δ1R⊕Δ2R⊕Δ3R⊕Δ4R, and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

Funder

Princess Nourah bint Abdulrahman University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/4/367/pdf

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