The construction of orbit codes based on singular linear space over finite fields

Orbit code is a class of constant dimension code which is defined as orbit of a subgroup of the general linear group G L „ (F g ), acting on the set of all the subspaces of vector space F£. In this paper, the construction of orbit codes based on the singular general linear group GLn+ (Fq) acting on the set of all the subspaces of type (m, k) in singular linear spaces Fqn+ is given. We give a characterization of orbit code constructed in singular linear space F £ + l , and then give some basic properties of the constructed orbit codes. Finally two examples about our orbit codes for understanding these properties explicitly are presented. © 2019 Charles Babbage Research Centre. All rights reserved.