Exceptional scattered polynomials

JOURNAL OF ALGEBRA

卷:509

Article

Bartoli, Daniele¹  Zhou, Yue² 

[1] Univ Perugia, Dept Math & Comp Sci, I-06123 Perugia, Italy

[2] Natl Univ Def Technol, Coll Liberal Arts & Sci, Changsha 410073, Hunan, Peoples R China

关键词: Maximum scattered linear set;    MRD code;    Algebraic curve;    Finite field;    Hasse-Weil bound;   

DOI  :  10.1016/j.jalgebra.2018.03.010

来源: Elsevier

【 摘 要 】

Let f be an F-q-linear function over F-qn. If the F-q-subspace U = {(x(qt), f (x)) : x is an element of F-qn} defines a maximum scattered linear set, then we call f a scattered polynomial of index t. As these polynomials appear to be very rare, it is natural to look for some classification of them. We say a function f is an exceptional scattered polynomial of index t if the subspace U associated with f defines a maximum scattered linear set in PG(1, q(mn)) for infinitely many m. Our main results are the classifications of exceptional scattered monic polynomials of index 0 (for q > 5) and of index 1. The strategy applied here is to convert the original question into a special type of algebraic curves and then to use the intersection theory and the Hasse-Weil theorem to derive contradictions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free