DeepAI AI Chat
Log In Sign Up

Abelian Noncyclic Orbit Codes and Multishot Subspace Codes

by   Gustavo Terra Bastos, et al.
University of Campinas
Federal University of Viçosa

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.


page 1

page 2

page 3

page 4


Skew Constacyclic and LCD Codes over F_q+v F_q

The aim of this paper is to give conditions for the equivalency between ...

Cyclic subspace codes via the sum of Sidon spaces

Subspace codes, especially cyclic constant subspace codes, are of great ...

Distance Distributions of Cyclic Orbit Codes

The distance distribution of a code is the vector whose i^th entry is th...

On cyclic LRC codes that are also LCD codes

Locally recoverable (LRC) codes provide a solution to single node failur...

Extended Cyclic Codes Sandwiched Between Reed-Muller Codes

The famous Barnes-Wall lattices can be obtained by applying Construction...

Binary Subspace Chirps

We describe in details the interplay between binary symplectic geometry ...

A Hierarchical-based Greedy Algorithm for Echelon-Ferrers Construction

Echelon-Ferrers is one of important techniques to help researchers to im...