Subspaces intersecting in at most a point

  • Sascha KurzEmail author


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.


Constant dimension codes Finite projective geometry Network coding 

Mathematics Subject Classification

Primary 51E20 Secondary 05B25 94B65 



The author would like to thank Thomas Honold for his analysis of possible clique sizes in the constant dimension codes from [9, Lemma 12, Example 4] and [8, Theorem 4], see Footnote 3. The main idea for Theorem 3 is inspired by [2]. Further thanks go to the anonymous referees for their careful reading and helpful remarks.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of BayreuthBayreuthGermany

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