Irreducible cyclic codes of length 4pn and 8pn

Fengwei Li; Qin Yue; Chengju Li

doi:10.1016/j.ffa.2015.01.009

Irreducible cyclic codes of length 4pⁿ and 8pⁿ

Fengwei Li^*
, Qin Yue
, Chengju Li

^*Corresponding author for this work

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

15 Scopus citations

Abstract

Let double-struck F_q be a finite field of q elements with q ≡ 3 (mod 8) and p|q - 1, where p is an odd prime. In this paper, we use matrix method to give all primitive idempotents in two rings double-struck F_q[x]/〈x^4pn - 1〉 and double-struck F_q[x]/〈x^8pn - 1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length 4pⁿ and 8pⁿ over double-struck F_q.

Original language	English
Pages (from-to)	208-234
Number of pages	27
Journal	Finite Fields and their Applications
Volume	34
DOIs	https://doi.org/10.1016/j.ffa.2015.01.009
State	Published - Jul 2015
Externally published	Yes

Keywords

Finite field
Irreducible cyclic code
Primitive idempotent

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10.1016/j.ffa.2015.01.009

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title = "Irreducible cyclic codes of length 4pn and 8pn",

abstract = "Let double-struck Fq be a finite field of q elements with q ≡ 3 (mod 8) and p|q - 1, where p is an odd prime. In this paper, we use matrix method to give all primitive idempotents in two rings double-struck Fq[x]/〈x4pn - 1〉 and double-struck Fq[x]/〈x8pn - 1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length 4pn and 8pn over double-struck Fq.",

keywords = "Finite field, Irreducible cyclic code, Primitive idempotent",

author = "Fengwei Li and Qin Yue and Chengju Li",

year = "2015",

month = jul,

doi = "10.1016/j.ffa.2015.01.009",

language = "英语",

volume = "34",

pages = "208--234",

journal = "Finite Fields and their Applications",

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T1 - Irreducible cyclic codes of length 4pn and 8pn

AU - Li, Fengwei

AU - Yue, Qin

AU - Li, Chengju

PY - 2015/7

Y1 - 2015/7

N2 - Let double-struck Fq be a finite field of q elements with q ≡ 3 (mod 8) and p|q - 1, where p is an odd prime. In this paper, we use matrix method to give all primitive idempotents in two rings double-struck Fq[x]/〈x4pn - 1〉 and double-struck Fq[x]/〈x8pn - 1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length 4pn and 8pn over double-struck Fq.

AB - Let double-struck Fq be a finite field of q elements with q ≡ 3 (mod 8) and p|q - 1, where p is an odd prime. In this paper, we use matrix method to give all primitive idempotents in two rings double-struck Fq[x]/〈x4pn - 1〉 and double-struck Fq[x]/〈x8pn - 1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length 4pn and 8pn over double-struck Fq.

KW - Finite field

KW - Irreducible cyclic code

KW - Primitive idempotent

UR - https://www.scopus.com/pages/publications/84923248086

U2 - 10.1016/j.ffa.2015.01.009

DO - 10.1016/j.ffa.2015.01.009

M3 - 文章

AN - SCOPUS:84923248086

SN - 1071-5797

VL - 34

SP - 208

EP - 234

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Irreducible cyclic codes of length 4pⁿ and 8pⁿ

Abstract

Keywords

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