有限域上代数乘法群的小生成集的构造

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation Pub Date : 2016-07-20 DOI:10.1145/2930889.2930921

Ming-Deh A. Huang, Lian Liu

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引用次数: 3

摘要

我们考虑有限域上代数的计算问题。特别地，我们提出了一种求GF(p)[x]/F的乘法群的小生成集的算法，其中p是素数，GF(p)[x]中的F是任意多项式。基于这一结果，可以显式地构造一组新的展开图。此外，我们提出了基的构造和给定元素相对于基的分解算法。

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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Constructing Small Generating Sets for the Multiplicative Groups of Algebras over Finite Fields

We consider computational problems concerning algebras over finite fields. In particular, we propose an algorithm for finding a small generating set for the multiplicative group of GF(p)[x]/F, where p is a prime number and F in GF(p)[x] is an arbitrary polynomial. Based on this result, a new set of expander graphs can be explicitly constructed. In addition, we present algorithms for basis construction and decomposition of a given element with respect to the basis.

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Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation

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