Subspaces intersecting in at most a point
Sascha Kurz · EPub Bayreuth (University of Bayreuth) · 2019
We improve on the lower bound of the maximum number of planes in $${\text {PG}}(8,q)\cong \mathbb {F}_q^{9}$$ 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.