Linear Maximum Rank Distance Codes of Exceptional Type

Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest the exceptional ones, as defined in 2018 by first author and Zhou, for which partial classification results known. In this paper we propose unified algebraic description $\mathbb {F}_{q^{n}}$ -linear maximum rank distance codes, introducing notion linear codes index. Such connection naturally extends exceptionality scattered polynomial metric framework provides generalization Moore sets monomial MRD context. We move towards showing that ones zero generalized Gabidulin proving positive case code contains an same