科研之友
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摘要
In this paper, we present a construction of linear codes over F-2(t) from Boolean functions, which is a generalization of Ding's method. Based on this construction, we give two classes of linear codes (C) over tilde (integral) and C-integral over F-2(t) from a Boolean function f : F-q -> F-2, where q = 2(n) and F-2(t) is some subfield of F-q. The complete weight enumerator of (C) over tilde (integral) can be easily determined from the Walsh spectrum of f, while the weight distribution of the code C-f can also be easily settled. Particularly, the number of nonzero weights of (C) over tilde (integral) and C f is the same as the number of distinct Walsh values of f. As applications of this construction, we show several series of linear codes over F-2(t) with two or three weights by using bent, semibent, monomial and quadratic Boolean function f.
