Large weight code words in projective space codes

Abstract: Recently, a large number of results have appeared on the small weights of the (dual) linear codes arising from finite projective spaces. We now focus on the large weights of these linear codes. For q even, this study for the code reduces to the theory of minimal blocking sets with respect to the k-spaces of , odd-blocking the k-spaces. For q odd, in a lot of cases, the maximum weight of the code is equal to , but some unexpected exceptions arise to this result. In particular, the maximum weight of the code turns out to be . In general, the problem of whether the maximum weight of the code , with (), is equal to , reduces to the problem of the existence of sets of points in intersecting every k-space in points. [Copyright &y& Elsevier]