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 codeswhichmight produce the largest non-sunflower codes. A novel construction, based on the Plücker embedding, for 1-intersecting codes of k-dimensional subspaces over Fq , n ≥ k+1 2  , where the code size is q k+1 −1 q−1 is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size n × n 2  over Fq, rank n − 1, and rank distance n − 1. © 2015 Elsevier B.V. All rights reserved.