The subfield codes of several classes of linear codes

Let F-2m be the finite field with 2(m) elements, where m is a positive integer. Recently, Heng and Ding in (Finite Fields Appl. 56:308-331, 2019) studied the subfield codes of two families of hyperovel codes and determined the weight distribution of the linear code C-a,C-b = {((Tr-1(m) (af (x) + bx) + c)(x is an element of F2m), Tr-1(m) (a), Tr-1(m) (b)) : a, b is an element of F-2m, c is an element of F-2}, for f (x) = x(2) and f (x) = x(6) with odd m. Let v(2)(.) denote the 2-adic order function. This paper investigates more subfield codes of linear codes and obtains the weight distribution of C-a,C-b for f (x) = x(2i+2j), where i, j are nonnegative integers such that v(2)(m) <= v(2)(i - j) (i >= j). In addition to this, we further investigate the punctured code of C-a,C-b as follows: C-a = {((Tr-1(m)(ax(2i+2j) + bx) + c)(x is an element of F2m), Tr-1(m)(a)) : a, b is an element of F-2m, c is an element of F-2}, and determine its weight distribution for any nonnegative integers i, j. The parameters of these binary linear codes are new in most cases. Some of the codes and their duals obtained are optimal or almost optimal.