The Hermitian Dual Codes of Several Classes of BCH Codes

Mengyuan Fan; Chengju Li; Cunsheng Ding

doi:10.1109/TIT.2023.3257123

The Hermitian Dual Codes of Several Classes of BCH Codes

Mengyuan Fan
, Chengju Li^*
, Cunsheng Ding

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q2 -ary BCH code of length n with respect to an n -th primitive root of unity β over an extension field of \Bbb F_q2 , and let C H denote its Hermitian dual code, where q is a prime power. If both C and C H are a BCH code with respect to an n -th primitive root of unity β , then C is called a Hermitian dually-BCH code. The objective of this paper is to derive a necessary and sufficient condition for ensuring that two classes of narrow-sense BCH codes are Hermitian dually-BCH codes. As by-products, lower bounds on the minimum distances of the Hermitian dual codes of these BCH codes are developed, which improve the lower bounds documented in IEEE Trans. Inf. Theory, vol. 68, no. 2, pp. 953-964, 2022, in some cases.

Original language	English
Pages (from-to)	4484-4497
Number of pages	14
Journal	IEEE Transactions on Information Theory
Volume	69
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2023.3257123
State	Published - 1 Jul 2023

Keywords

BCH code
Hermitian dually-BCH code
cyclic code
linear code

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10.1109/TIT.2023.3257123

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title = "The Hermitian Dual Codes of Several Classes of BCH Codes",

abstract = "As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q2 -ary BCH code of length n with respect to an n -th primitive root of unity β over an extension field of \textbackslash{}Bbb F\_q2 , and let C H denote its Hermitian dual code, where q is a prime power. If both C and C H are a BCH code with respect to an n -th primitive root of unity β , then C is called a Hermitian dually-BCH code. The objective of this paper is to derive a necessary and sufficient condition for ensuring that two classes of narrow-sense BCH codes are Hermitian dually-BCH codes. As by-products, lower bounds on the minimum distances of the Hermitian dual codes of these BCH codes are developed, which improve the lower bounds documented in IEEE Trans. Inf. Theory, vol. 68, no. 2, pp. 953-964, 2022, in some cases.",

keywords = "BCH code, Hermitian dually-BCH code, cyclic code, linear code",

author = "Mengyuan Fan and Chengju Li and Cunsheng Ding",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2023",

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doi = "10.1109/TIT.2023.3257123",

language = "英语",

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T1 - The Hermitian Dual Codes of Several Classes of BCH Codes

AU - Fan, Mengyuan

AU - Li, Chengju

AU - Ding, Cunsheng

PY - 2023/7/1

Y1 - 2023/7/1

N2 - As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q2 -ary BCH code of length n with respect to an n -th primitive root of unity β over an extension field of \Bbb F_q2 , and let C H denote its Hermitian dual code, where q is a prime power. If both C and C H are a BCH code with respect to an n -th primitive root of unity β , then C is called a Hermitian dually-BCH code. The objective of this paper is to derive a necessary and sufficient condition for ensuring that two classes of narrow-sense BCH codes are Hermitian dually-BCH codes. As by-products, lower bounds on the minimum distances of the Hermitian dual codes of these BCH codes are developed, which improve the lower bounds documented in IEEE Trans. Inf. Theory, vol. 68, no. 2, pp. 953-964, 2022, in some cases.

AB - As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q2 -ary BCH code of length n with respect to an n -th primitive root of unity β over an extension field of \Bbb F_q2 , and let C H denote its Hermitian dual code, where q is a prime power. If both C and C H are a BCH code with respect to an n -th primitive root of unity β , then C is called a Hermitian dually-BCH code. The objective of this paper is to derive a necessary and sufficient condition for ensuring that two classes of narrow-sense BCH codes are Hermitian dually-BCH codes. As by-products, lower bounds on the minimum distances of the Hermitian dual codes of these BCH codes are developed, which improve the lower bounds documented in IEEE Trans. Inf. Theory, vol. 68, no. 2, pp. 953-964, 2022, in some cases.

KW - BCH code

KW - Hermitian dually-BCH code

KW - cyclic code

KW - linear code

UR - https://www.scopus.com/pages/publications/85151521301

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DO - 10.1109/TIT.2023.3257123

M3 - 文章

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VL - 69

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EP - 4497

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 7

ER -

The Hermitian Dual Codes of Several Classes of BCH Codes

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Keywords

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