On the code generated by the incidence matrix of points and k-spaces in PG(n,q) and its dual

In this paper, we study the p-ary linear code Ck(n,q), q=ph, p prime, h⩾1, generated by the incidence matrix of points and k-dimensional spaces in PG(n,q). For k⩾n/2, we link codewords of Ck(n,q)∖Ck⊥(n,q) of weight smaller than 2qk to k-blocking sets. We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all codewords arising from small linear k-blocking sets. For k