Abelian Noncyclic Orbit Codes and Multishot Subspace Codes
Information Theory
2018-10-19 v1 math.IT
Abstract
In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, the Abelian orbit codes are defined and a new construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As a consequence, a substantial reduction in the number of computations needed to obtain the minimum subspace distance of these codes is achieved and established. An application of orbit codes to multishot subspace codes obtained according to a multi-level construction is provided.
Keywords
Cite
@article{arxiv.1810.08049,
title = {Abelian Noncyclic Orbit Codes and Multishot Subspace Codes},
author = {Gustavo Terra Bastos and Reginaldo Palazzo Júnior and Marinês Guerreiro},
journal= {arXiv preprint arXiv:1810.08049},
year = {2018}
}