On the classification of exceptional scattered polynomials

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:179

Article

Bartoli, Daniele¹  Montanucci, Maria² 

[1] Univ Perugia, Dipartimento Matemat & Informat, Perugia, Italy

[2] Tech Univ Denmark, Dept Appl Math & Comp Sci, Asmussens Alle,Bldg 303B, DK-2800 Lyngby, Denmark

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

DOI  :  10.1016/j.jcta.2020.105386

来源: Elsevier

【 摘 要 】

Let f(X) is an element of F-qr[X] be a q-polynomial. If the F-q-subspace U = {(x(qt), f(x)) vertical bar x is an element of F-qn} defines a maximum scattered linear set, then we call f(X) a scattered polynomial of index t. The asymptotic behavior of scattered polynomials of index t is an interesting open problem. In this sense, exceptional scattered polynomials of index tare those for which U is a maximum scattered linear set in PG(1, q(mr)) for infinitely many m. The classifications of exceptional scattered monic polynomials of index 0(for q > 5) and of index 1 were obtained in [1]. In this paper we complete the classifications of exceptional scattered monic polynomials of index 0 for q <= 4. Also, some partial classifications are obtained for arbitrary t. As a consequence, the classification of exceptional scattered monic polynomials of index 2 is given. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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