Subspaces intersecting in at most a point

Abstract

We improve on the lower bound of the maximum number of planes in $\operatorname{PG}(8,q)\cong\F_q^{9}$ pairwise intersecting in at most a point. In terms of constant dimension codes this leads to $A_q(9,4;3)\ge q^{12}+2q^8+2q^7+q^6+2q^5+2q^4-2q^2-2q+1$. This result is obtained via a more general construction strategy, which also yields other improvements.

4 pages

References in corpus (3)

• Partial spreads and vector space partitions
• On putative q-Analogues of the Fano Plane and Related Combinatorial Structures
• Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6