In this paper we completely characterize the words with second minimum weight in the p−ary linear code generated by the rows of the incidence matrix of points and hyperplanes of PG(n,q), with q=ph and p prime, proving that they are the scalar multiples of the difference of the incidence vectors of two distinct hyperplanes of PG(n,q).
@article{arxiv.1606.02222,
title = {Codes arising from incidence matrices of points and hyperplanes in $PG(n,q)$},
author = {Olga Polverino and Ferdinando Zullo},
journal= {arXiv preprint arXiv:1606.02222},
year = {2016}
}