On the sunflower bound for k-spaces, pairwise intersecting in a point
Abstract
A t-intersecting constant dimension subspace code C is a set of k-dimensional subspaces in a projective space PG (n, q) , where distinct subspaces intersect in exactly a t-dimensional subspace. A classical example of such a code is the sunflower, where all subspaces pass through the same t-space. The sunflower bound states that such a code is a sunflower if |C|>(qk+1-qt+1q-1)2+(qk+1-qt+1q-1)+1. In this article we will look at the case t= 0 and we will improve this bound for q≥ 9 : a set S of k-spaces in PG (n, q) , q≥ 9 , pairwise intersecting in a point is a sunflower if |S|>(2q6+4q3-5q)(qk+1-1q-1)2.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Blokhuis, A., De Boeck, M., & D’haeseleer, J. (2022). On the sunflower bound for k-spaces, pairwise intersecting in a point. Designs, Codes, and Cryptography, 90 (9), 2101-2111. https://doi.org/10.1007/s10623-021-00949-6
