A NOTE ON FULL WEIGHT SPECTRUM CODES

A linear [n; k]q code C is said to be a full weight spectrum (FWS) code if there exist codewords of each weight less than or equal to n. In this brief communication we determine necessary and sufficient conditions for the existence of linear [n; k]q full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in PG(k - 1; q).