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Cryptography and Communications

Erschienen in:

06.11.2019

A class of constacyclic BCH codes

verfasst von: Zhonghua Sun, Shixin Zhu, Liqi Wang

Erschienen in: Cryptography and Communications | Ausgabe 2/2020

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Abstract

Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum distance of a class of q-ary constacyclic BCH codes of length \(\frac {q^{m}-1}{q-1}\) with designed distances \(\delta _{i}=q^{m-1}-\frac {q^{\lfloor \frac {m-3}2 \rfloor +i }-1}{q-1}\) for \(1\leq i\leq \min \limits \{\lceil \frac {m+1}2 \rceil -\lfloor \frac {m}{q+1} \rfloor , \lceil \frac {m-1}2 \rceil \}\). As will be seen, some of these codes are optimal.

Vorheriger Artikel -additive cyclic codes are asymptotically good

Nächster Artikel On the minimum weights of binary linear complementary dual codes

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Titel: A class of constacyclic BCH codes
verfasst von: Zhonghua Sun
Shixin Zhu
Liqi Wang
Publikationsdatum: 06.11.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 2/2020
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00401-6

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