Codes with few weights arising from linear sets (Q6112236)

In this paper, a class of linear codes with few weights arising from a special type of linear sets is presented. The authors show that h-scattered linear sets of maximum rank provide families of point sets with few intersection numbers with respect to hyperplanes, yielding codes (equipped with Hamming distance) with few weights. In addition, the weight of such codes, their weight enumerators and possible choices for their generator matrices are derived. In particular, it is shown how this general construction yields to obtain linear codes with three weights which are almost MDS codes.