The Asymptotic Behavior of Grassmannian Codes

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...

Codes and designs in Grassmannian spaces

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...

The Weight Distribution of a Family of Lagrangian-Grassmannian Codes

Using Plücker coordinates we construct a matrix whose columns parametrize all projective isotropic lines in a symplectic space E of dimension 4 over a finite field Fq. As an application of this construction we explicitly obtain the smallest subfamily of algebro-geometric codes defined by the corresponding Lagrangian-Grassmannian variety. Furthermore, we show that this subfamily is a class of th...

Weight spectrum of codes associated with the Grassmannian G(3,7)

In this paper we consider the problem of determining the weight spectrum of q-ary codes C(3,m) associated with Grassmann varieties G(3,m). For m = 6 this was done in [1]. We derive a formula for the weight of a codeword of C(3,m), in terms of certain varieties associated with alternating trilinear forms on F q . The classification of such forms under the action of the general linear group GL(m,...