Several families of subfield codes from special functions and elliptic quadric

Recently, subfield codes of linear codes over finite fields have garnered significant interest since some of these codes are optimal. In this paper, we present several new families of binary few-weight subfield codes from special functions and a new family of subfield codes from elliptic quadric. Moreover, we prove that some of these subfield codes are self-orthogonal and explicitly determine the parameters of their duals. The duals of these infinite families of subfield codes presented in this paper are optimal or almost optimal with respect to the Sphere-packing bound.