期刊
FINITE FIELDS AND THEIR APPLICATIONS
卷 18, 期 4, 页码 781-790出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2012.02.003
关键词
Permutation polynomial; Finite field; Piecewise function
资金
- National Basic Research Program of China [2007CB311201]
- National Natural Science Foundation of China [61070172, 10990011, 11071107]
Two classes of permutation polynomials over finite fields are presented. The first class is a further study of permutation polynomials of the form (x(pk) - x + delta)(s) + L(x) and the second class is a supplement of the recent work of Hou on permutation polynomials. We show the permutation properties of two polynomials in the first class and five polynomials in the second class by using their implicit or explicit piecewise function characteristic over the subsets of the finite field defined by multiplicative or additive characters of the field. Two polynomials in the first class theoretically explain two numerical observations of J. Yuan et al. in their permutation polynomial search experiment. (C) 2012 Elsevier Inc. All rights reserved.
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