2019/07/11 by Rakhi Pratihar, Pratihar, Rakhi, Tovohery Hajatiana Randrianarisoa +1 · 1 citation
Computer Science · Mathematics · #15A03 #94B05 #94B60 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1907.05508
openalex publication_date 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.