A family of linear codes with few weights and their subfield codes.

Linear codes with few weights have many applications in secret sharing, strongly regular graphs, association schemes and authentication codes. Recently, subfield codes of some linear codes with few weights have been studied. In this paper, we present a family of linear codes with few weights and their punctured codes, whose parameters and weight distributions are completely determined. And we give the parameters of their dual codes, which are length-optimal and dimensional-optimal with respect to the Sphere-packing bound. In addition, we also investigate their subfield codes to obtain some q-ary linear codes with few weights. The weight distributions and dualities of these subfield codes are explicitly determined. [ABSTRACT FROM AUTHOR]