Linear codes meeting the Griesmer bound, minihypers and geometric applications

Abstract

Coding theory and Galois geometries are two research areas which greatly influence each other. In this talk, we focus on the link between linear codes meeting the Griesmer bound and minihypers in finite projective spaces. Minihypers are particular (multiple) blocking sets. We present characterization results on minihypers, leading to equivalent characterization results on linear codes meeting the Griesmer bound. Next to being interesting from a coding-theoretical point of view, minihypers also are interesting for geometrical applications. We present results on maximal partial μ-spreads in PG(N, q), (μ + 1)|(N + 1), on minimal μ-covers in PG(N, q), (μ + 1)|(N + 1), on (N − 1)-covers of Q + (2N + 1, q), on partial ovoids and on partial spreads of finite classical polar spaces, and on partial ovoids of generalized hexagons, following from results on minihypers.