A Construction of Linear Codes over $\f_{2^t}$ from Boolean Functions

In this paper, we present a construction of linear codes over F2t from Boolean functions, which is a generalization of Ding’s method [1, Theorem 9]. Based on this construction, we give two classes of linear codes C̃ f and C f (see Theorem 1 and Theorem 6) over F2t from a Boolean function f : Fq → F2, where q = 2n and F2t is some subfield of Fq. The complete weight enumerator of C̃ f 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 C̃ f 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 F2t with two or three weights by using bent, semibent, monomial and quadratic Boolean function f .