Improvement to the sunflower bound for a class of equidistant constant dimension subspace codes (Q2035132)

An equidistant constant dimension subspace code (\((k,t)\)-SCID) \(C\) consists of a set of \(k\)-dimensional subspaces of a vector space over a finite field such that each pair intersect in a subspace of a fixed dimension \(t\). The classical example of such a code is a set of \(k\)-spaces, passing through a fixed \(t\)-space, which is called a sunflower. The authors improve the sunflower bound by proving the following. If \( |C| \geq \left(\frac{q^k-q}{q-1}\right)^2 + \frac{q^k-q}{q-1}-q^{k-1}\), then \(C\) is a sunflower.