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Research Article

QUANTUM CODES THROUGH CONSTACYCLIC CODES OVER $\mathcal{F}_{p}+{\mu}\mathcal{F}_{p}+{\nu}\mathcal{F}_{p}+{\varpi}\mathcal{F}_{p}+{\mu}{\nu}\mathcal{F}_{p}+{\nu}{\varpi}\mathcal{F}_{p}+{\mu}{\varpi}\ma

R
Rekha Kumawat Department of Mathematics, Maharshi Dayanand University, Rohtak - 124001, Haryana, INDIA
M
Monika Sangwan Department of Mathematics, Maharshi Dayanand University, Rohtak - 124001, Haryana, INDIA
Volume 21, Issue 3 Pages 349-360 December 30, 2025 1 downloads
Article overview

Abstract

The purpose of this paper is to identify the structural characteristics and construction of quantum codes over $\mathcal{F}_p$ using $\alpha_1+\alpha_2 {\mu}+\alpha_3 {\nu}+\alpha_4 {\varpi}+\alpha_5 {\mu}{\nu}+\alpha_6 {\nu}{\varpi}+\alpha_7 {\mu}{\varpi}+\alpha_8 {\mu}{\nu}{\varpi}- $constacyclic codes over ring $\mathcal{R} ~= ~\mathcal{F}_p[{\mu},{\nu},{\varpi}]/<{\mu}^2-{\mu}, {\nu}^2-{\nu}, {\varpi}^2-{\varpi}~, {\mu}{\nu}-{\nu}{\mu}, {\nu}{\varpi}-{\varpi}{\nu}, {\mu}{\varpi}-{\varpi}{\mu}>$, here $\mathcal F_{p}$ is a finite field with p elements. We define a Gray map from $\mathcal{R}$ to $\mathcal{F}_p^{8}$, a distance-preserving map. Breaking down constacyclic codes into cyclic and negacyclic codes results in the creation of quantum codes over the finite field $\mathcal{F}_p$. As an application, some examples are illustrated to obtain the quantum codes of different parameters.

Keywords and Phrases

Gray mapcyclic codesconstacyclic codesnegacyclic codes.

AMS Subject Classification

94B05, 94B15, 94B60.

Reference information

How to Cite

Rekha Kumawat, Monika Sangwan (2025). QUANTUM CODES THROUGH CONSTACYCLIC CODES OVER $\mathcal{F}_{p}+{\mu}\mathcal{F}_{p}+{\nu}\mathcal{F}_{p}+{\varpi}\mathcal{F}_{p}+{\mu}{\nu}\mathcal{F}_{p}+{\nu}{\varpi}\mathcal{F}_{p}+{\mu}{\varpi}\ma. South East Asian Journal of Mathematics and Mathematical Sciences, 21(3), 349-360.
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