Constacyclic Codes Over 𝑭𝒒[𝒖] /〈𝒖𝟑 = 𝟎〉 and Their Application of Constructing Quantum Codes

Year 2022, Volume: 5 Issue: 2, 12 - 22, 16.01.2023

Zineb Hebbache

https://doi.org/10.53508/ijiam.1127019

Abstract

Let 𝑅 = 𝐹𝑞+u𝐹𝑞+𝑢^2𝐹𝑞, 𝑢^3=0 be a finite chain ring. In this paper, we give the structure of constacyclic codes over 𝑅 and obtain self-orthogonal codes over 𝐹𝑞 by using the Gray map from 𝑅𝑛 to 𝐹𝑞^(3𝑛). As an application, we present a construction of quantum codes from the codes obtained from this class.

Keywords

Constacyclic codes, Gray map, Euclidean self-orthogonal, quantum codes.

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