Equidistant codes in the Grassmannian

Equidistant codes over vector spaces are considered. For k-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. Anovel construction, based on the Plücker embedding, for 1-intersecting codes of k-dimensional subspaces over Fⁿ_q, n ≥ (^k+1₂), where the code size is ^qk+1-1/_q-1 is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size n × (ⁿ₂) over F_q, rank n - 1, and rank distance n - 1.