A class of subfield codes of linear codes and their duals

摘要

Recently, subfield codes of some optimal linear codes have been studied. In this paper, we further investigate a class of subfield codes and generalize the results of the subfield codes of the conic codes in Ding and Wang (Finite Fields Appl.56, 308-331,2020). The weight distributions of these subfield codes and the parameters of their duals are determined. Some of the presented codes are optimal or almost optimal according to Grassl (2020) and their duals are distance-optimal with respect to the Sphere Packing bound ifp 3. As a byproduct, we directly obtain the weight distributions of the punctured codes, which is the same with the results presented in Du et al. (2019a,b), and determine the parameters of the duals of the punctured codes. These dual codes are distance-optimal with respect to the Sphere Packing bound with rare exceptions.