A note on the stability of trinomials over finite fields

被引：5

作者：

Ahmadi, Omran ^{[1
]}

Monsef-Shokri, Khosro ^{[2
]}

机构：

[1] Inst Res Fundamental Sci IPM, Tehran, Iran

[2] Shahid Beheshti Univ, Dept Math Sci, Tehran, Iran

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2020年 / 63卷

关键词：

Polynomials; Iterations; Stability; Finite fields; IRREDUCIBLE POLYNOMIALS;

D O I：

10.1016/j.ffa.2020.101649

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A polynomial f (x) over a field K is called stable if all of its iterates are irreducible over K. In this paper, we study the stability of trinomials over finite fields. We show that if f (x) is a trinomial of even degree over the binary field F-2, then (x) is not stable. We prove similar results for some families of monic trinomials over finite fields of odd characteristic. We also study the stability of polynomials of higher weights and prove some results and pose a new conjecture. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：13

共 22 条

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