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Applicable Algebra in Engineering, Communication and Computing

Erschienen in:

06.09.2021 | Original Paper

A new algorithm for equivalence of cyclic codes and its applications

verfasst von: Nuh Aydin, R. Oliver VandenBerg

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 4/2023

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Abstract

Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems related to cyclic codes. In this work, we use recent results on the equivalence of cyclic codes to create a more efficient algorithm to partition cyclic codes by equivalence based on cyclotomic cosets. This algorithm is then implemented to carry out computer searches for both cyclic codes and quasi-cyclic (QC) codes with good parameters. We also generalize these results to repeated-root cases. We have found several new linear codes that are cyclic or QC as an application of the new approach, as well as more desirable constructions for linear codes with best known parameters. With the additional new codes obtained through standard constructions, we have found a total of 14 new linear codes.

Vorheriger Artikel AG codes from -rational points of the GK maximal curve

Nächster Artikel Deterministic factoring with oracles

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Titel: A new algorithm for equivalence of cyclic codes and its applications
verfasst von: Nuh Aydin
R. Oliver VandenBerg
Publikationsdatum: 06.09.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Applicable Algebra in Engineering, Communication and Computing / Ausgabe 4/2023
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-021-00525-4

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