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In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields. Moreover, we characterize all these cyclotomic permutation polynomials that are involutions. Our results provide a fast algorithm (only modular operations are involved) to generate many classes of generalized cyclotomic permutation polynomials, their inverses, and involutions. 相似文献
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Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication theory and so on. Permutation binomials and permutation trinomials attract people's interest due to their simple algebraic forms and additional extraordinary properties. In this paper, we find a new result about permutation binomials and construct several new classes of permutation trinomials. Some of them are generalizations of known ones. 相似文献
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In this paper, we propose several classes of permutation polynomials based on trace functions over finite fields of characteristic 2. The main result of this paper is obtained by determining the number of solutions of certain equations over finite fields. 相似文献
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Tim PenttilaJason Williford 《Journal of Combinatorial Theory, Series A》2011,118(2):502-509
In this paper, we construct the first known infinite family of primitive Q-polynomial schemes which are not generated by distance-regular graphs. To construct these examples, we introduce the notion of a relative hemisystem of a generalized quadrangle with respect to a subquadrangle. 相似文献
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In this paper, we completely determine all necessary and sufficient conditions such that the polynomial , where , is a permutation quadrinomial of over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial , where and and proposed some new classes of permutation quadrinomials of .In particular, in this paper we classify all permutation polynomials of of the form , where , over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. 相似文献
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Greg Stein. 《Mathematics of Computation》2001,70(235):1237-1251
We examine the problem of factoring the th cyclotomic polynomial, over , and distinct primes. Given the traces of the roots of we construct the coefficients of in time . We demonstrate a deterministic algorithm for factoring in time when has precisely two irreducible factors. Finally, we present a deterministic algorithm for computing the sum of the irreducible factors of in time .
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We study the explicit factorization of 2
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r-th cyclotomic polynomials over finite field
\mathbbFq{\mathbb{F}_q} where q, r are odd with (r, q) = 1. We show that all irreducible factors of 2
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r-th cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders. In particular,
we obtain the explicit factorization of 2
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5-th cyclotomic polynomials over finite fields and construct several classes of irreducible polynomials of degree 2
n–2 with fewer than 5 terms. 相似文献
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Akihide Hanaki 《Journal of Combinatorial Theory, Series A》2008,115(2):226-236
We give a definition of nilpotent association schemes as a generalization of nilpotent groups and investigate their basic properties. Moreover, for a group-like scheme, we characterize the nilpotency by its character products. 相似文献