Weight distributions of cyclic codes with respect to pairwise coprime order elements

Chengju Li; Qin Yue; Fengwei Li

doi:10.1016/j.ffa.2014.01.009

Weight distributions of cyclic codes with respect to pairwise coprime order elements

Chengju Li^*
, Qin Yue
, Fengwei Li

^*Corresponding author for this work

Nanjing University of Aeronautics and Astronautics
SKL of Mathematical Engineering and Advanced Computing
Zaozhuang University

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

105 Scopus citations

Abstract

Let ^Fr be an extension of a finite field F_q with r=q^m. Let each ^gi be of order ⁿⁱ in _r^* and gcd(ⁿⁱ,^nj)=1 for 1≤i≠j≤u. We define a cyclic code over F_q byC(q,m, ⁿ¹,ⁿ²,.,^nu)={C(^a1, ^a2,.,^au):a₁,a₂,.,a _u⋯^Fr}, whereC(^a1,^a2,., ^au)=(Trr/_q(Σi=1u^aigi0),.,Trr/ _q(Σi=1u^aigin-1)) and n=ⁿ¹ ⁿ²⋯^nu. In this paper, we present a method to compute the weights of C(q,m,ⁿ¹,ⁿ²,.,^nu). Further, we determine the weight distributions of the cyclic codes C(q,m, ⁿ¹,ⁿ²) and C(q,m,ⁿ¹,ⁿ²,1).

Original language	English
Pages (from-to)	94-114
Number of pages	21
Journal	Finite Fields and their Applications
Volume	28
DOIs	https://doi.org/10.1016/j.ffa.2014.01.009
State	Published - Jul 2014
Externally published	Yes

Keywords

Character sums
Cyclic codes
Gauss periods
Weight distribution

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10.1016/j.ffa.2014.01.009

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@article{8608e03f672c46e19a4e6419257cc76e,

title = "Weight distributions of cyclic codes with respect to pairwise coprime order elements",

abstract = "Let Fr be an extension of a finite field Fq with r=qm. Let each gi be of order ni in r* and gcd(ni,nj)=1 for 1≤i≠j≤u. We define a cyclic code over Fq byC(q,m, n1,n2,.,nu)=\{C(a1, a2,.,au):a1,a2,.,a u⋯Fr\}, whereC(a1,a2,., au)=(Trr/q(Σi=1uaigi0),.,Trr/ q(Σi=1uaigin-1)) and n=n1 n2⋯nu. In this paper, we present a method to compute the weights of C(q,m,n1,n2,.,nu). Further, we determine the weight distributions of the cyclic codes C(q,m, n1,n2) and C(q,m,n1,n2,1).",

keywords = "Character sums, Cyclic codes, Gauss periods, Weight distribution",

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

year = "2014",

month = jul,

doi = "10.1016/j.ffa.2014.01.009",

language = "英语",

volume = "28",

pages = "94--114",

journal = "Finite Fields and their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Weight distributions of cyclic codes with respect to pairwise coprime order elements

AU - Li, Chengju

AU - Yue, Qin

AU - Li, Fengwei

PY - 2014/7

Y1 - 2014/7

N2 - Let Fr be an extension of a finite field Fq with r=qm. Let each gi be of order ni in r* and gcd(ni,nj)=1 for 1≤i≠j≤u. We define a cyclic code over Fq byC(q,m, n1,n2,.,nu)={C(a1, a2,.,au):a1,a2,.,a u⋯Fr}, whereC(a1,a2,., au)=(Trr/q(Σi=1uaigi0),.,Trr/ q(Σi=1uaigin-1)) and n=n1 n2⋯nu. In this paper, we present a method to compute the weights of C(q,m,n1,n2,.,nu). Further, we determine the weight distributions of the cyclic codes C(q,m, n1,n2) and C(q,m,n1,n2,1).

AB - Let Fr be an extension of a finite field Fq with r=qm. Let each gi be of order ni in r* and gcd(ni,nj)=1 for 1≤i≠j≤u. We define a cyclic code over Fq byC(q,m, n1,n2,.,nu)={C(a1, a2,.,au):a1,a2,.,a u⋯Fr}, whereC(a1,a2,., au)=(Trr/q(Σi=1uaigi0),.,Trr/ q(Σi=1uaigin-1)) and n=n1 n2⋯nu. In this paper, we present a method to compute the weights of C(q,m,n1,n2,.,nu). Further, we determine the weight distributions of the cyclic codes C(q,m, n1,n2) and C(q,m,n1,n2,1).

KW - Character sums

KW - Cyclic codes

KW - Gauss periods

KW - Weight distribution

UR - https://www.scopus.com/pages/publications/84896859311

U2 - 10.1016/j.ffa.2014.01.009

DO - 10.1016/j.ffa.2014.01.009

M3 - 文章

AN - SCOPUS:84896859311

SN - 1071-5797

VL - 28

SP - 94

EP - 114

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Weight distributions of cyclic codes with respect to pairwise coprime order elements

Abstract

Keywords

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