Some constructions of cyclic and quasi-cyclic subspaces codes

TL;DR

This paper constructs cyclic and quasi-cyclic subspace codes using computational algebra tools, including an optimal code over F_{2^{10}} and a new q-analogous code over F_{2^{8}}.

Contribution

It introduces new constructions of cyclic and quasi-cyclic subspace codes, including an optimal code and a novel q-analogous definition with examples.

Findings

Constructed an optimal cyclic subspace code over F_{2^{10}}.

Defined and provided an example of a q-analogous m-quasi-cyclic subspace code over F_{2^{8}}.

Abstract

In this paper we construct, using GAP System for Computational Discrete Algebra, some cyclic subspace codes, specially an optimal code over the finite field F_{2^{10}}. Further we present a definition and an example of the $q$-analogous of a $m$-quasi-cyclic subspace code over F_{2^{8}}.