A Construction of Orbit Codes

Abstract

Given a finite field $$\mathbb {F}_{q}$$ , a constant dimension code is a set of k-dimensional subspaces of $$\mathbb {F}_{q}^{n}$$ . Orbit codes are constant dimension codes which are defined as orbits when the action of a subgroup of the general linear group on the set of all subspaces of $$\mathbb {F}_{q}^{n}$$ is considered. In this paper we present a construction of an Abelian non-cyclic orbit code whose minimum subspace distance is maximal.