On weighted { δv μ + 1 , δv μ ; k − 1 , q } - minihypers , q square

Weighted minihypers have recently received a lot of attention. They originated as geometrical equivalents of linear codes meeting the Griesmer bound, but have also been investigated for their importance in solving geometrical problems. Storme characterized weighted {δ(q+1), δ; k−1, q}-minihypers, q square, as a sum of lines and Baer subgeometries PG(3, √ q), provided δ is sufficiently small. This result is the basis for a new characterization result on weighted {δvμ+1, δvμ; k− 1, q}-minihypers. We show that such minihypers are a sum of μ-dimensional subspaces and of (projected) (2μ+1)-dimensional Baer subgeometries PG(2μ+1, √ q). Because of the equivalence of minihypers with linear codes meeting the Griesmer bound, a new contribution to the characterization of linear codes meeting the Griesmer bound is also obtained.