Codes arising from incidence matrices of points and hyperplanes in $PG(n,q)$

摘要

In this paper we completely characterize the words with second minimum weightin the $p-$ary linear code generated by the rows of the incidence matrix ofpoints and hyperplanes of $PG(n,q)$, with $q=p^h$ and $p$ prime, proving thatthey are the scalar multiples of the difference of the incidence vectors of twodistinct hyperplanes of $PG(n,q)$.