A class of subfield codes of linear codes and their duals

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 if p > 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.

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