A Construction of Linear Codes Over ${\mathbb {F}}_{2^t}$ From Boolean Functions
Can Xiang, Keqin Feng, Chunming Tang · IEEE Transactions on Information Theory · 2016
In this paper, we present a construction of linear codes over F2tfrom Boolean functions, which is a generalization of Ding's method. Based on this construction, we give two classes of linear codes C̃fand Cfover F2tfrom a Boolean function f : Fq→ F2, where q = 2nand F2tis some subfield of Fq. The complete weight enumerator of C̃fcan be easily determined from the Walsh spectrum of f , while the weight distribution of the code Cfcan also be easily settled. Particularly, the number of nonzero weights of C̃fand 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 F2twith two or three weights by using bent, semibent, monomial and quadratic Boolean function f.