A Construction of Linear Codes Over ${\mathbb {F}}_{2^t}$ From Boolean Functions

In this paper, we present a construction of linear codes over F
_2t
from Boolean functions, which is a generalization of Ding's method. Based on this construction, we give two classes of linear codes C̃
_f
and C
_f
over F
_2t
from a Boolean function f : F
_q
→ F
₂
, where q = 2
ⁿ
and F
_2t
is some subfield of F
_q
. 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 F
_2t
with two or three weights by using bent, semibent, monomial and quadratic Boolean function f.