Linear sets and MRD-codes arising from a class of scattered linearized polynomials
Giovanni Longobardi, Corrado Zanella

TL;DR
This paper introduces a new class of scattered linearized polynomials over finite fields, leading to novel maximum scattered linear sets and infinite families of MRD-codes with specific parameters.
Contribution
It generalizes a known polynomial construction to arbitrary even dimensions and establishes new scattered linear sets and MRD-code families.
Findings
Constructed new scattered linearized polynomials for all even n ≥ 6.
Produced new maximum scattered linear sets in PG(1, q^n) for n=8,10.
Developed infinite families of MRD-codes with minimum distance n-1.
Abstract
A class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the -polynomial over , described in arXiv:1906.05611, arXiv:1910.02278 is generalized for any even to an -linear automorphism of of order . Such and some functional powers of it are proved to be scattered. In particular this provides new maximum scattered linear sets of the projective line for . The polynomials described in this paper lead to a new infinite family of MRD-codes in with minimum distance for any odd if and any if .
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