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 -