Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

cyclic orbit codes with the normalizer of a singer subgroup

an algebraic construction for constant dimension subspace codes is called orbit code. it arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. in particular orbit codes of a singer subgroup of the general linear group has investigated recently. in this paper, we consider the normalizer of a singer subgroup of the general linear group a...

Plücker Embedding of Cyclic Orbit Codes

Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Plücker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.

Plücker Embedding of Cyclic Orbit Codes

Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Plücker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words. 1. Introduction. In network coding one is looking at the transmission of information through a directed graph with possibly several senders and several receivers [1]. One c...

Cyclic orbit codes and stabilizer subfields

Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given subspace is a vector space, the cardinality of the orbit code can be determined, and estimates for its distance can be found. This subfield is closely related to...

A Complete Characterization of Irreducible Cyclic Orbit Codes

Constant dimension codes are subsets of the finite Grassmann variety. The study of constant dimension codes with good distances have been central in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are characterized that the elements of the code can be viewed as the orbit under a group action. The paper gives a complete characterization of ...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes