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 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). (C) 2018 Elsevier Inc. All rights reserved.