Axioms (Apr 2023)

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

  • Shakir Ali,
  • Amal S. Alali,
  • Mohammad Jeelani,
  • Muhammet Kurulay,
  • Elif Segah Öztas,
  • Pushpendra Sharma

DOI
https://doi.org/10.3390/axioms12040367
Journal volume & issue
Vol. 12, no. 4
p. 367

Abstract

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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.

Keywords