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

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 \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes \tilde{\C}_{f} and \C_f (see Theorem \ref{thm-maincode1} and Theorem \ref{thm-maincodenew}) over \f_{2^t} from a Boolean function f:\f_{q}\rightarrow \f_2, where $q=2^n$ and \f_{2^t} is some subfield of \f_{q}. The complete weight enumerator of \tilde{\C}_{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 \tilde{\C}_{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 \f_{2^t} with two or three weights by using bent, semibent, monomial and quadratic Boolean function $f$