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Applicable Algebra in Engineering, Communication and Computing
Erschienen in: Applicable Algebra in Engineering, Communication and Computing 6/2023

20.10.2021 | Original Paper

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

verfasst von: Hai Q. Dinh, Bac T. Nguyen, Roengchai Tansuchat

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 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.
Vorheriger Artikel An identification system based on the explicit isomorphism problem
Nächster Artikel Interleavings and matchings as representations

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Metadaten
Titel
Quantum MDS and synchronizable codes from cyclic codes of length over
verfasst von
Hai Q. Dinh
Bac T. Nguyen
Roengchai Tansuchat
Publikationsdatum
20.10.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing / Ausgabe 6/2023
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00531-6

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