Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, two families of binary subfield codes with a few weights are presented from two special classes of linear codes, and their parameters are explicitly determined. Moreover, the parameters of the duals of these subfield codes are also studied. The two infinite families of subfield codes presented in this paper are distance-optimal with respect to the Griesmer bound and their duals are almost distance-optimal with respect to the sphere-packing bound.

有限域上的线性代码的子域代码最近受到了广泛的关注，因为其中一些代码是最优的，并在秘密共享，身份验证代码和关联方案中得到应用。本文从两类特殊的线性代码中提出了两个权重较小的二进制子域代码家族，并明确确定了它们的参数。此外，还研究了这些子场代码的对偶的参数。本文介绍的两个无限子域代码族相对于Griesmer界是距离最优的，而它们的对偶相对于球面堆积界是距离最优的。