Parameters for which the Griesmer bound is not sharp

7 We prove for a large class of parameters t and r that a multiset of at most t d−k + r d−k−2 points in PG(d, q) that blocks every k-dimensional subspace at least t times must contain a sum of t subspaces of codimension k. 9 We use our results to identify a class of parameters for linear codes for which the Griesmer bound is not sharp. Our theorem generalizes the non-existence results from Maruta [On the achievement of the Griesmer bound, Des. Codes Cryptogr. 12 (1997) 11 83–87] and Klein [On codes meeting the Griesmer bound, Discrete Math. 274 (2004) 289–297]. © 2007 Published by Elsevier B.V. 13