Parameters of several families of binary duadic codes and their related codes

Hai Liu; Chengju Li; Haifeng Qian

doi:10.1007/s10623-023-01285-7

Parameters of several families of binary duadic codes and their related codes

Hai Liu
, Chengju Li^*
, Haifeng Qian

^*Corresponding author for this work

Software Engineering Institute

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

9 Scopus citations

Abstract

Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2 ^m- 1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Designs, Codes, and Cryptography
Volume	92
Issue number	1
DOIs	https://doi.org/10.1007/s10623-023-01285-7
State	Published - Jan 2024

Keywords

Cyclic code
Duadic code
Linear code
Self-dual code

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10.1007/s10623-023-01285-7

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abstract = "Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2 m- 1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.",

keywords = "Cyclic code, Duadic code, Linear code, Self-dual code",

author = "Hai Liu and Chengju Li and Haifeng Qian",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s10623-023-01285-7",

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T1 - Parameters of several families of binary duadic codes and their related codes

AU - Liu, Hai

AU - Li, Chengju

AU - Qian, Haifeng

PY - 2024/1

Y1 - 2024/1

N2 - Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2 m- 1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

AB - Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2 m- 1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

KW - Cyclic code

KW - Duadic code

KW - Linear code

KW - Self-dual code

UR - https://www.scopus.com/pages/publications/85172109486

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JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 1

ER -

Parameters of several families of binary duadic codes and their related codes

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Keywords

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