TY - JOUR
T1 - Complete weight enumerators of a class of linear codes
AU - Ahn, Jaehyun
AU - Ka, Dongseok
AU - Li, Chengju
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - Let Fq be the finite field with q= pm elements, where p is an odd prime and m is a positive integer. For a positive integer t, let D⊂Fqt and let Tr m be the trace function from Fq onto Fp. In this paper, let D={(x1,x2,…,xt)∈Fqt\{(0,0,…,0)}:Trm(x1+x2+⋯+xt)=0}, we define a p-ary linear code CD by CD={c(a1,a2,…,at):(a1,a2,…,at)∈Fqt},where c(a1,a2,…,at)=(Trm(a1x12+a2x22+⋯+atxt2))(x1,x2,…,xt)∈D.We shall present the complete weight enumerators of the linear codes CD and give several classes of linear codes with a few weights. This paper generalizes the results of Yang and Yao (Des Codes Cryptogr, 2016).
AB - Let Fq be the finite field with q= pm elements, where p is an odd prime and m is a positive integer. For a positive integer t, let D⊂Fqt and let Tr m be the trace function from Fq onto Fp. In this paper, let D={(x1,x2,…,xt)∈Fqt\{(0,0,…,0)}:Trm(x1+x2+⋯+xt)=0}, we define a p-ary linear code CD by CD={c(a1,a2,…,at):(a1,a2,…,at)∈Fqt},where c(a1,a2,…,at)=(Trm(a1x12+a2x22+⋯+atxt2))(x1,x2,…,xt)∈D.We shall present the complete weight enumerators of the linear codes CD and give several classes of linear codes with a few weights. This paper generalizes the results of Yang and Yao (Des Codes Cryptogr, 2016).
KW - Gauss sums
KW - Linear codes
KW - Weight distribution
UR - https://www.scopus.com/pages/publications/84963651456
U2 - 10.1007/s10623-016-0205-8
DO - 10.1007/s10623-016-0205-8
M3 - 文章
AN - SCOPUS:84963651456
SN - 0925-1022
VL - 83
SP - 83
EP - 99
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1
ER -