Covering of Subspaces by Subspaces

Details Covering of Subspaces by Subspaces Covering of Subspaces by Subspaces

2011-11-18

arxiv.org/abs/1111.4319v2

Mathematics

Combinatorics

Scientific paper

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph $\cG_q(n,r)$ by subspaces from the Grassmann graph $\cG_q(n,k)$, $k \geq r$, are discussed. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and a recursive construction. We discuss the density of these coverings. Tables for the best known coverings, for $q=2$ and $5 \leq n \leq 10$, are presented. We present some questions concerning possible constructions of new coverings of smaller size.

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