Subspaces intersecting in at most a point

07/05/2019

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by   Sascha Kurz, et al.

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We improve on the lower bound of the maximum number of planes in PG(8,q)_q^9 pairwise intersecting in at most a point. In terms of constant dimension codes this leads to A_q(9,4;3)> 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.