Some new non-additive maximum rank distance codes
type: Item
instance of: scholarly article
title: Some new non-additive maximum rank distance codes
zbMATH Open document ID: 1454.94138
author: Kamil Otal
author: Ferruh Özbudak
published in: Finite Fields and their Applications
publication date: 2018-02-15T00:00:00Z
review text: Most of the maximum rank distance (MRD) codes in the literature are additively closed and, in previous works, only one construction of not additively closed codes is introduced [\textit{A. Cossidente} et al., Des. Codes Cryptography 79, No. 3, 597--609 (2016; Zbl 1386.94112)] (and its generalization [\textit{N. Durante} and \textit{A. Siciliano}, Electron. J. Comb. 24, No. 2, Research Paper P2.33, 18 p. (2017; Zbl 1366.94585)]), working for some certain parameters. In this paper, the authors introduce a new construction of MRD codes as a generalization of generalized Gabidulin codes which are not additively closed when the basis field has odd characteristics. Moreover, such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters.
reviewed by: Marco Calderini
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 6839001
zbMATH Keywords: rank metric codes
zbMATH Keywords: maximum rank distance (MRD) codes
zbMATH Keywords: additive generalized twisted Gabidulin codes
zbMATH Keywords: linearized polynomials
MaRDI profile type: Publication
full work available at URL: j.ffa.2017.12.003
OpenAlex ID: W2778570824
cites work: Algebraic structures of MRD codes
cites work: Non-linear maximum rank distance codes
cites work: Bilinear forms over a finite field, with applications to coding theory
cites work: Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries
cites work: Theory of codes with maximum rank distance
cites work: Q4037491
cites work: Galois theory and linear algebra
cites work: Generalized twisted Gabidulin codes
cites work: New criteria for MRD and Gabidulin codes and some rank-metric code constructions
cites work: Explicit constructions of some non-Gabidulin linear maximum rank distance codes
cites work: Additive Rank Metric Codes
cites work: Maximum-rank array codes and their application to crisscross error correction
cites work: A new family of linear maximum rank distance codes
cites work: A Rank-Metric Approach to Error Control in Random Network Coding
cites work: Space-time codes for high data rate wireless communication: performance criterion and code construction
cites work: Q4885576
DOI: 10.1016/J.FFA.2017.12.003
description: scientific article; zbMATH DE number 6839001