Algebraic Properties of Permutation Polynomials (Special Section on Discrete Mathematics and Its Applications)
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概要
- 論文の詳細を見る
Polynomials are called permutation polynomials if they induce bijective functions. This paper investigates algebraic properties of permutation polynomials over a finite field, especially properties associated with permutation cycles. A permutation polynomial has a simple structure but good randomness properties suitable for applications. The cycle structure of permutations are considered to be related to randomness. We investigate the algebraic structure from the viewpoint of randomness. First we show the relationship between polynomials and permutations using a matrix equation. Then, we give a general form of a permutation polynomial corresponding to a product C_1 C_2…C_k of pairwise disjoint cycles. Finally, permutation polynomials with fixed points -or with 2, 3 and 4-cycles- and their compositions are given together with distribution of degree of the permutation polynomials.
- 一般社団法人電子情報通信学会の論文
- 1996-04-25
著者
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OKAMOTO Eiji
School of Engineering, Hokkaido Tokai University
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Aitken Wayne
Department Of Mathematics California State University
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BLAKLEY George
Department of Mathematics, Texas A&M University
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Blakley George
Department Of Mathematics Texas A&m University
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