A class of linear codes with two weights or three weights from some planar functions

作者：Zhu, Xiaoxing^*; Yang, Fengfan

来源：Journal of Applied Mathematics and Computing, 2018, 56(1-2): 235-252.

DOI：10.1007/s12190-016-1071-2

• Linear codes
• Weight distribution
• Guass sum
• Weil sum

Let F-q be a finite field with q = p(m) elements, where p is an odd prime and m is a positive integer. In this paper, let D = {(x(1), x(2), . . . , x(n)) is an element of F-q(n) \{(0, 0, . . .)} : Tr(x(1)(pk1+1) + x(2)(pk2+1) + . . . + x(n)(pkn+1)) = c}, where c is an element of F-p, Tr is the trace function from F-q to F-p and each m/(m, ki) (1 <= i <= n) is odd. we define a p-ary linear code C-D = {c(a(1), a(2), . . . , a(n)) : (a(1), a(2),. . ., a(n)). F-q(n)}, where c(a(1), a(2), . . . , a(n)) = (Tr(a(1)x(1) + a(2)x(2)+ . . . + a(n)x(n)))(x(1), x(2), . . . , x(n)) is an element of D. We present the weight distributions of the classes of linear codes which have at most three weights.

• 出版日期2018-2
• 单位南京航空航天大学