Subspaces intersecting in at most a point

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Kurz, Sascha:
Subspaces intersecting in at most a point.
Bayreuth , 2019 . - 4 S.

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Abstract

We improve on the lower bound of the maximum number of planes in PG(8,q) pairwise intersecting in at most a point. In terms of constant dimension codes this leads to A<sub>q(9,4;3) ≥ q¹² + 2q⁸ + 2q⁷ + q⁶ + 2q⁵ + 2q⁴ - 2q² - 2q + 1. This result is obtained via a more general construction strategy, which also yields other improvements.