A generalization of the normal rational curve in PG(d, q~n) and its associated non-linear MRD codes

摘要

Let A and B be two points of and let be a collineation between the stars of lines with vertices A and B, that does not map the line AB into itself. In this paper we prove that if or and the lines are not in a common plane, then the set of points of intersection of corresponding lines under is the union of scattered -linear sets of rank n together with . As an application we will construct, starting from the set , infinite families of non-linear -MRD codes, , generalizing those recently constructed in Cossidente et al. (Des Codes Cryptogr 79:597-609, 2016) and Durante and Siciliano (Electron J Comb, 2017).