Self-duality of generalized twisted Gabidulin codes

Kamil Otal, Ferruh Özbudak, Wolfgang Willems
2018 Advances in Mathematics of Communications  
Self-duality of Gabidulin codes was investigated in [10] and the authors provided an if and only if condition for a Gabidulin code to be equivalent to a self-dual maximum rank distance (MRD) code. In this paper, we investigate the analog problem for generalized twisted Gabidulin codes (a larger family of linear MRD codes including the family of Gabidulin codes). We observe that the condition presented in [10] still holds for generalized Gabidulin codes (an intermediate family between Gabidulin
more » ... odes and generalized twisted Gabidulin codes). However, beyond the family of generalized Gabidulin codes we observe that some additional conditions are required depending on the additional parameters. Our tools are similar to those in [10] but we also use linearized polynomials, which leads to further tools and direct proofs. 2010 Mathematics Subject Classification: Primary: 11T71; Secondary: 94B05.
doi:10.3934/amc.2018042 fatcat:qubwpwhs6rb5rhplavnjxl3xxe