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2024 | OriginalPaper | Chapter

Quantum Codes Over an Extension of \({\mathbb {Z}_4}\)

Authors : Mohammad Ashraf, Naim Khan, Washiqur Rehman, Ghulam Mohammad

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

Let \(\mathfrak {A}=\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4,\) where \(u^2=u\), \(v^2=v\) and \(uv=vu=0\) be a ring, which is an extension of \(\mathbb {Z}_{4}\). In this article, we study the structure of cyclic codes over the ring \(\mathfrak {A}\) and define a \(\mathbb Z_2\)-linear isometry \(\Phi \) from \(\mathfrak {A}^{n}\) to \(\mathbb Z^{6n}_2.\) Based on the classical cyclic codes, we construct binary quantum codes by utilizing Gray images of cyclic codes over \(\mathfrak {A}\). As an application, we provide some examples of binary quantum error-correcting codes.

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previous chapter Results on Generalized Derivations in Prime Rings with Involution

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Title: Quantum Codes Over an Extension of
Authors: Mohammad Ashraf
Naim Khan
Washiqur Rehman
Ghulam Mohammad
Publisher: Springer Nature Switzerland
Book: Advances in Ring Theory and Applications
Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50795-3_27

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