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Applicable Algebra in Engineering, Communication and Computing
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20-10-2021 | Original Paper

Quantum MDS and synchronizable codes from cyclic codes of length \(5p^s\) over \(\mathbb F_{p^m}\)

Authors: Hai Q. Dinh, Bac T. Nguyen, Roengchai Tansuchat

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2023

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Abstract

For any odd prime \(p\not =5\), the structures of cyclic codes of length \(5p^s\) over \(\mathbb F_{p^m}\) are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.
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Metadata
Title
Quantum MDS and synchronizable codes from cyclic codes of length over
Authors
Hai Q. Dinh
Bac T. Nguyen
Roengchai Tansuchat
Publication date
20-10-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 6/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00531-6

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