Matrices in M2[Fq[T]] with quadratic minimal polynomial

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-01-16 DOI:10.1016/j.ffa.2024.102361

Jacobus Visser van Zyl

引用次数: 0

Abstract

By a result of Latimer and MacDuffee, there are a finite number of equivalence classes of $n \times n$ matrices over $F_{q} [T]$ with minimum polynomial $p (X)$ , where p is an $n^{th}$ degree polynomial, irreducible over $F_{q} [T]$ . In this paper, we develop an algorithm for finding a canonical representative of each matrix class, for $p (X) = X^{2} - Γ X - Δ \in F_{q} [T] [X]$ .

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M2[Fq[T]] 中具有二次最小多项式的矩阵

根据 Latimer 和 MacDuffee 的一个结果，Fq[T] 上 n×n 矩阵有有限个等价类，其最小多项式为 p(X)，其中 p 是 Fq[T] 上不可约的 n 次多项式。本文开发了一种算法，用于为 p(X)=X2-ΓX-∈ΔFq[T][X] 找到每个矩阵类的典型代表。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.