A construction of Abelian non-cyclic orbit codes

A constant dimension code consists of a set of k-dimensional subspaces of Fnq, where Fq is a finite field of q elements. Orbit codes are constant dimension codes which are defined as orbits under the action of a subgroup of the general linear group on the set of all k-dimensional subspaces of Fnq. If the acting group is Abelian, we call the corresponding orbit code Abelian orbit code. In this paper we present a construction of an Abelian non-cyclic orbit code for which we compute its cardinality and its minimum subspace distance. Our code is a partial spread and consequently its minimum subspace distance is maximal.This work was partially supported by Spanish grants AICO/2017/128 of the Generalitat Valenciana and VIGROB287 of the Universitat d’Alacant