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. A novel construction, based on the Pl\"{u}cker
embedding, for 1-intersecting codes of k-dimensional subspaces over \F_q^n,
nβ₯(2k+1β), where the code size is qβ1qk+1β1β is
presented. Finally, we present a related construction which generates
equidistant constant rank codes with matrices of size nΓ(2nβ)
over \F_q, rank nβ1, and rank distance nβ1.Comment: 16 page