Climent, Joan-Josep, Requena Arévalo, Verónica, Soler-Escrivà, Xaro
A construction of Abelian non-cyclic orbit codes
Cryptography and Communications. 2019, 11(5): 839-852. doi:10.1007/s12095-018-0306-5
URI: http://hdl.handle.net/10045/95511
DOI: 10.1007/s12095-018-0306-5
ISSN: 1936-2447 (Print)
Abstract: 
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.
Keywords:Random linear network coding, Subspace codes, Grassmannian, Group action, General linear group, Abelian group
Springer US
info:eu-repo/semantics/article