Constructions of cyclic constant dimension codes

Constructions of cyclic constant dimension codes

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional properties that can be applied efficiently in encoding and decoding algorithms. It is desirable to find cyclic constant dimension codes such that both the code ...

Isotropic Constant Dimension Subspace Codes

 In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...

New LMRD bounds for constant dimension codes and improved constructions

Let V ∼= Fq be a v-dimensional vector space over the finite field Fq with q elements. By [ V k ] we denote the set of all k-dimensional subspaces in V . Its size is given by the q-binomial coefficient [ v k ]q = ∏k−1 i=0 qv−qi qk−qi for 0 ≤ k ≤ v and 0 otherwise. The set of all subspaces of V forms a metric space associated with the so-called subspace distance dS(U,W ) = dim(U + W ) − dim(U ∩ W...

Constructions of binary constant-weight cyclic codes and cyclically permutable codes

A general theorem is proved showing how to ohtain a constant-weight binary cyclic code from a p-ary linear cyclic code, where p is a prime,. by using a representation of Cl;(p) as cyclic shifts of a binary p-tuple. Based on this theorem, constructions are given for four classes of binary constant-weight codes. The first two classes are shown to achieve the Johnson upper bound on minimum distanc...

On the Constructions of Constant-Weight Codes