Tim Alderson - University of New Brunswick

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-۱,q) $.

weight spectrum, linear code, Hamming weight, FWS, MWS