On quasi-cyclic subspace codes

Some constructions of subspaces cyclic and quasi-cyclic codes

In this paper we construct, using GAP System for Computational Discrete Algebra, some cyclic subspace codes, specially an optimal code over the finite field F210 . Further we present a definition and an example of the q-analogous of a m-quasi-cyclic subspace code over F28 .

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

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...

On the Codes over a Semilocal Finite Ring

In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error corr...

On quasi-cyclic codes as a generalization of cyclic codes

In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length lm and ideals of Ml(Fq)[X]/(X m −1). This permits to construct new classes of codes, namely quasi-BCH and quasi-evaluation codes. We study th...