Some new non-additive maximum rank distance codes
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.
additive generalized twisted Gabidulin codes
scientific article; zbMATH DE number 6839001
scientific article