Emergent Mind
Constructions of optimal rank-metric codes from automorphisms of rational function fields
(1907.05508)
Published Jul 11, 2019
in
cs.IT
and
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.
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