Quantum codes from the cyclic codes over Fp[u,v,w]/⟨u2−1,v2−1,w2−1,uv−vu,vw−wv,wu−uw⟩

Islam, Habibul; Prakash, Om

doi:10.1007/s12190-018-01230-1

Published June 1, 2019 | Version v1

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Quantum codes from the cyclic codes over $F_{p} [u, v, w] / ⟨ u^{2} - 1, v^{2} - 1, w^{2} - 1, u v - v u, v w - w v, w u - u w ⟩$

1. Indian Institute of Technology Patna, Department of Mathematics (India)

In this article, for any odd prime p, we construct the quantum codes over $F_{p}$ by using the cyclic codes of length n over $R = F_{p} [u, v, w] / ⟨ u^{2} - 1, v^{2} - 1, w^{2} - 1, u v - v u, v w - w v, w u - u w ⟩$ . We obtain the self-orthogonal properties of cyclic codes over R and as an application, present some new quantum codes.

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DOI: 10.1007/s12190-018-01230-1;

Journal Title: Journal of Applied Mathematics and Computing (Internet)
Journal Volume: 60
Journal Issue: 1-2
Journal Page Range: p. 625-635
ISSN: 1865-2085

Country of Publication: Germany
Country of Input or Organization: International Atomic Energy Agency (IAEA)
INIS RN: 54087993
Subject category: S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI: MAPS; QUANTUM STATES; QUANTUM SYSTEMS

Copyright: Copyright (c) 2019 Korean Society for Computational and Applied Mathematics

Quantum codes from the cyclic codes over $F_{p} [u, v, w] / ⟨ u^{2} - 1, v^{2} - 1, w^{2} - 1, u v - v u, v w - w v, w u - u w ⟩$

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Quantum codes from the cyclic codes over Fp[u,v,w]/⟨u2−1,v2−1,w2−1,uv−vu,vw−wv,wu−uw⟩

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Quantum codes from the cyclic codes over $F_{p} [u, v, w] / ⟨ u^{2} - 1, v^{2} - 1, w^{2} - 1, u v - v u, v w - w v, w u - u w ⟩$