Equidistant codes in the Grassmannian

Equidistant codes over vector spaces are considered. For kk-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codes which might produce the largest non-sunflower codes. A novel construction, based on the Plücker embedding, for 1-intersecting codes of kk-dimensional subspaces over Fqn, n≥(k+12), where the code size is qk+1−1q−1 is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size n×(n2) over FqFq, rank n−1n−1, and rank distance n−1n−1.