Constructions of optimal rank-metric codes from automorphisms of rational function fields
Information Theory
2021-08-30 v4 math.IT
Abstract
We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first construction is of generalized Gabidulin codes over rational function fields. Reducing these codes over finite fields, we obtain maximum rank distance (MRD) codes which are not equivalent to generalized twisted Gabidulin codes. We also construct optimal Ferrers diagram rank-metric codes which settles further a conjecture by Etzion and Silberstein.
Cite
@article{arxiv.1907.05508,
title = {Constructions of optimal rank-metric codes from automorphisms of rational function fields},
author = {Rakhi Pratihar and Tovohery Hajatiana Randrianarisoa},
journal= {arXiv preprint arXiv:1907.05508},
year = {2021}
}
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37 pages