New Constructions of Orbit Codes Based on the Operations of Orbit Codes

An orbit code is a special constant dimension subspace code, which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space. This paper presents some methods of constructing new orbit codes from known orbit codes. Firstly, we introduce the sum operation, intersection operation and union operation of subspace codes, and then we give some methods to obtain new orbit codes from known orbit codes by fully applying the sub-orbits of permutation groups and the direct product operation of the groups. Finally, as a special application, partial spread codes are researched and a condition of orbit codes with constant distance is given.