Grassmannian codes from paired difference sets

Grassmannian Packings From Operator Reed-Muller Codes

This paper introduces multidimensional generalizations of binary Reed–Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for bi...

Difference Sets and Codes in $ A_n $ Lattices

This paper presents a geometric/coding theoretic interpretation of planar difference sets and the corresponding reformulations of two important conjectures in the field. It is shown that such sets of order n exist if and only if theAn lattice admits a lattice tiling by balls of radius 2 under l1 metric (i.e., a linear 2-perfect code). More general difference sets and perfect codes of larger rad...

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 cod...

Perfect difference sets constructed from Sidon sets

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...

Codes and designs in Grassmannian spaces