The Subfield Codes of Some Few-Weight Linear Codes
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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, the q-ary subfield codes C̅_f,g^(q) of six different families of linear codes C̅_f,g are presented, respectively. The parameters and weight distribution of the subfield codes and their punctured codes C̅_f,g^(q) are explicitly determined. The parameters of the duals of these codes are also studied. Some of the resultant q-ary codes C̅_f,g^(q), C̅_f,g^(q) and their dual codes are optimal and some have the best known parameters. The parameters and weight enumerators of the first two families of linear codes C̅_f,g are also settled, among which the first family is an optimal two-weight linear code meeting the Griesmer bound, and the dual codes of these two families are almost MDS codes. As a byproduct of this paper, a family of [2^4m-2,2m+1,2^4m-3] quaternary Hermitian self-dual code are obtained with m ≥ 2. As an application, several infinite families of 2-designs and 3-designs are also constructed with three families of linear codes of this paper.
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