论有限域上多项式的广义斐波那契序列

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-05-15 DOI:10.1016/j.ffa.2024.102446

Zekai Chen, Min Sha, Chen Wei

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引用次数: 0

摘要

在本文中，作为整数情况的类比，我们详细研究了有限域上任意多项式模的广义斐波那契序列的周期和秩。我们建立了一些公式来计算它们，还获得了它们商的一些性质。我们发现多项式情况比整数情况复杂得多。

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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On the generalized Fibonacci sequences of polynomials over finite fields

In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequences of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute them, and we also obtain some properties about their quotient. We find that the polynomial case is much more complicated than the integer case.

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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.