On some cyclic codes of length [Formula presented]

Peng Wu; Chengju Li; Wei Peng

doi:10.1016/j.ffa.2019.101581

On some cyclic codes of length [Formula presented]

Peng Wu, Chengju Li^*, Wei Peng

^*Corresponding author for this work

Software Engineering Institute

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

11 Scopus citations

Abstract

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to investigate the parameters of some q-ary cyclic codes of length n= [Formula presented]. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented by employing the Hartmann-Tzeng bound or BCH bound. Moreover, when q=2,3, we give the largest coset leaders δ₁ modulo n and investigate the parameters of the BCH codes C_{(q,n,δ₁,1)}.

Original language	English
Article number	101581
Journal	Finite Fields and their Applications
Volume	60
DOIs	https://doi.org/10.1016/j.ffa.2019.101581
State	Published - Nov 2019

Keywords

BCH code
Coset leader
Cyclic code
Cyclotomic coset
Hartmann-Tzeng bound

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10.1016/j.ffa.2019.101581

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title = "On some cyclic codes of length [Formula presented] ",

abstract = "Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to investigate the parameters of some q-ary cyclic codes of length n= [Formula presented]. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented by employing the Hartmann-Tzeng bound or BCH bound. Moreover, when q=2,3, we give the largest coset leaders δ1 modulo n and investigate the parameters of the BCH codes C(q,n,δ1,1).",

keywords = "BCH code, Coset leader, Cyclic code, Cyclotomic coset, Hartmann-Tzeng bound",

author = "Peng Wu and Chengju Li and Wei Peng",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - Wu, Peng

AU - Li, Chengju

AU - Peng, Wei

PY - 2019/11

Y1 - 2019/11

N2 - Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to investigate the parameters of some q-ary cyclic codes of length n= [Formula presented]. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented by employing the Hartmann-Tzeng bound or BCH bound. Moreover, when q=2,3, we give the largest coset leaders δ1 modulo n and investigate the parameters of the BCH codes C(q,n,δ1,1).

AB - Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to investigate the parameters of some q-ary cyclic codes of length n= [Formula presented]. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented by employing the Hartmann-Tzeng bound or BCH bound. Moreover, when q=2,3, we give the largest coset leaders δ1 modulo n and investigate the parameters of the BCH codes C(q,n,δ1,1).

KW - BCH code

KW - Coset leader

KW - Cyclic code

KW - Cyclotomic coset

KW - Hartmann-Tzeng bound

UR - https://www.scopus.com/pages/publications/85071878748

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DO - 10.1016/j.ffa.2019.101581

M3 - 文章

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SN - 1071-5797

VL - 60

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

M1 - 101581

ER -

On some cyclic codes of length [Formula presented]

Abstract

Keywords

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