A linear [n,k]qβ code C is said to be a full weight spectrum (FWS)
code if there exist codewords of each nonzero weight less than or equal to n. In this brief communication we determine necessary and sufficient conditions
for the existence of linear [n,k]qβ 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(kβ1,q)