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...

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...

In network coding, a flag code is set of sequences nested subspaces $${{\mathbb {F}}}_q^n$$ , being {F}}}_q$$ the finite field with q elements. Flag codes defined as orbits cyclic subgroup general linear group acting on flags are called orbit codes. Inspired by ideas in Gluesing-Luerssen et al. (Adv Math Commun 9(2):177–197, 2015), we determine cardinality and provide bounds for its distance he...

We introduce a new class of constant dimension codes called orbit codes. The basic properties of these codes are derived. It will be shown that many of the known families of constant dimension codes in the literature are actually orbit codes. DOI: https://doi.org/10.1109/CIG.2010.5592788 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh...

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...

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 ...

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...

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a subgroup of the general linear group on the Grassmannian. This paper gives a complete characterization of orbit codes that are generated by an irredu...

The distance distribution of a code is the vector whose ith entry number pairs codewords with i. We investigate structure for cyclic orbit codes, which are subspace codes generated by action $${\mathbb {F}}_{q^n}^*$$ on an {F}}_q$$ -subspace U {F}}_{q^n}$$ . Note that Singer cycle in general linear group all -automorphisms show full-length maximal possible depends only $$q,\,n$$ , and dimension...