TY - JOUR
T1 - Three classes of linear codes with two or three weights
AU - Heng, Ziling
AU - Yue, Qin
AU - Li, Chengju
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/11/6
Y1 - 2016/11/6
N2 - In this paper, we mainly determine the weight distributions of three classes of linear codes. Firstly, we prove that two classes of ternary linear codes from the following two planar functions have two or three weights: f(x)=x3k+12,x∈F3m, where k,m are odd, gcd(m,k)=1, and f(x)=x3k+1,x∈F3m, where mgcd(m,k) is odd. They are exactly a part of the open problem in Ding and Ding (2015 Section IV). Secondly, we construct a new class of binary linear codes with three weights. In particular, the linear codes in this paper have applications in consumer electronics, communication and secret sharing schemes.
AB - In this paper, we mainly determine the weight distributions of three classes of linear codes. Firstly, we prove that two classes of ternary linear codes from the following two planar functions have two or three weights: f(x)=x3k+12,x∈F3m, where k,m are odd, gcd(m,k)=1, and f(x)=x3k+1,x∈F3m, where mgcd(m,k) is odd. They are exactly a part of the open problem in Ding and Ding (2015 Section IV). Secondly, we construct a new class of binary linear codes with three weights. In particular, the linear codes in this paper have applications in consumer electronics, communication and secret sharing schemes.
KW - Gauss sum
KW - Linear code
KW - Quadratic form
KW - Weight distribution
UR - https://www.scopus.com/pages/publications/84975138678
U2 - 10.1016/j.disc.2016.05.033
DO - 10.1016/j.disc.2016.05.033
M3 - 文章
AN - SCOPUS:84975138678
SN - 0012-365X
VL - 339
SP - 2832
EP - 2847
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 11
ER -