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

An equidistant constant dimension subspace code C is a set of k-dimensional subspaces in a vector space V over the finite field of order q, which pairwise intersect in subspaces of a fixed dimension t. The classical example of an equidistant constant dimension subspace code C is a set of k-spaces, passing through a fixed t-space. This particular example is called a sunflower. The sunflower bound states that if the size of C is larger than $$\left( \frac{q^{k}-q^{t}}{q-1}\right) ^2 + \frac{q^{k}-q^{t}}{q-1} +1$$ , then C is a sunflower. We improve this sunflower bound for an equidistant constant dimension subspace code C of k-spaces, pairwise intersecting in a 1-space.