Two families of negacyclic BCH codes

Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let q be an odd prime power and m be a positive integer. The objective of this paper is to study negacyclic BCH codes with length q...

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Published in:Designs, codes, and cryptography codes, and cryptography, 2023-07, Vol.91 (7), p.2395-2420
Main Authors: Wang, Xiaoqiang, Sun, Zhonghua, Ding, Cunsheng
Format: Article
Language:English
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BCH codes
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Fields (mathematics)
Parameters
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description Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let q be an odd prime power and m be a positive integer. The objective of this paper is to study negacyclic BCH codes with length q m - 1 2 and q m + 1 2 over the finite field GF ( q ) and analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certain q and m , compared with cyclic codes with the same dimension and length, the negacyclic BCH codes presented in this paper have a larger minimum distance in some cases.
doi_str_mv 10.1007/s10623-023-01208-6
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subjects BCH codes
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Fields (mathematics)
Parameters
title Two families of negacyclic BCH codes
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