The minimum Hamming distances of irreducible cyclic codes

Fengwei Li; Qin Yue; Chengju Li

doi:10.1016/j.ffa.2014.05.003

The minimum Hamming distances of irreducible cyclic codes

Fengwei Li^*
, Qin Yue
, Chengju Li

^*Corresponding author for this work

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

20 Scopus citations

Abstract

Let ^Fq be a finite field with q elements and n=l1 ^m1l2^m2, ^m1≤1, ^m2≥1, where ^l1, ^l2 are distinct primes and l1 l2 |q-1. In this paper, we give all irreducible factors of xl1m1l2 m2-1 over ^Fq and all primitive idempotents in a ring ^Fq[x]/〈xl1 m1 l2 m2 -1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1^m1l2^m2 over ^Fq.

Original language	English
Pages (from-to)	225-242
Number of pages	18
Journal	Finite Fields and their Applications
Volume	29
DOIs	https://doi.org/10.1016/j.ffa.2014.05.003
State	Published - Sep 2014
Externally published	Yes

Keywords

Finite field
Irreducible cyclic code
Primitive idempotent

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10.1016/j.ffa.2014.05.003

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title = "The minimum Hamming distances of irreducible cyclic codes",

abstract = "Let Fq be a finite field with q elements and n=l1 m1l2m2, m1≤1, m2≥1, where l1, l2 are distinct primes and l1 l2 |q-1. In this paper, we give all irreducible factors of xl1m1l2 m2-1 over Fq and all primitive idempotents in a ring Fq[x]/〈xl1 m1 l2 m2 -1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1m1l2m2 over Fq.",

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

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

year = "2014",

month = sep,

doi = "10.1016/j.ffa.2014.05.003",

language = "英语",

volume = "29",

pages = "225--242",

journal = "Finite Fields and their Applications",

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T1 - The minimum Hamming distances of irreducible cyclic codes

AU - Li, Fengwei

AU - Yue, Qin

AU - Li, Chengju

PY - 2014/9

Y1 - 2014/9

N2 - Let Fq be a finite field with q elements and n=l1 m1l2m2, m1≤1, m2≥1, where l1, l2 are distinct primes and l1 l2 |q-1. In this paper, we give all irreducible factors of xl1m1l2 m2-1 over Fq and all primitive idempotents in a ring Fq[x]/〈xl1 m1 l2 m2 -1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1m1l2m2 over Fq.

AB - Let Fq be a finite field with q elements and n=l1 m1l2m2, m1≤1, m2≥1, where l1, l2 are distinct primes and l1 l2 |q-1. In this paper, we give all irreducible factors of xl1m1l2 m2-1 over Fq and all primitive idempotents in a ring Fq[x]/〈xl1 m1 l2 m2 -1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1m1l2m2 over Fq.

KW - Finite field

KW - Irreducible cyclic code

KW - Primitive idempotent

UR - https://www.scopus.com/pages/publications/84901703938

U2 - 10.1016/j.ffa.2014.05.003

DO - 10.1016/j.ffa.2014.05.003

M3 - 文章

AN - SCOPUS:84901703938

SN - 1071-5797

VL - 29

SP - 225

EP - 242

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

The minimum Hamming distances of irreducible cyclic codes

Abstract

Keywords

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