Quasi-optimal cyclic orbit codes
Information Theory
2025-01-08 v1 Combinatorics
math.IT
Abstract
We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the codewords of a cyclic orbit code and a certain linear set on the projective line. This allows us to derive new bounds on the parameters of the code. In the second part, we study a particular family of (quasi-)optimal cyclic orbit codes and derive a general existence theorem for quasi-optimal codes in even-dimensional vector spaces over finite fields of any characteristic. Finally, for our particular code family we describe the automorphism groups under the general linear group and a suitable Galois group.
Cite
@article{arxiv.2501.03802,
title = {Quasi-optimal cyclic orbit codes},
author = {Chiara Castello and Heide Gluesing-Luerssen and Olga Polverino and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2501.03802},
year = {2025}
}