Netanel Raviv – Equidistant codes in the Grassmannian


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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?cker embedding, for 1-intersecting codes of k-dimensional subspaces over Fqn, n ?{k+1 \choose 2}, where the code size is is presented. We also present a related construction of equidistant rank-metric codes, which is to the best of our knowledge the first explicit construction of equidistant rank-metric codes.