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 nonzero weight less than or equal to $n$. In this brief communication we determine necessary and sufficient conditions for the existence of linear $[n,k]_q$ 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 $PG(k-1,q)$.

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