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

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 = p h 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 ) . [ABSTRACT FROM AUTHOR]