Large classes of permutation polynomials over Fq2
Permutation polynomials (PPs) of the form (xq-x + c)q2-1/3+1 + x over Fq2 were presented by Li et al.(Finite Fields Appl 22:16-23,2013).More recently,we have constructed PPs of the form (xq + bx + c)q2-1/d+1-bx over Fq2,where d =2,3,4,6 (Yuan and Zheng in Finite Fields Appl 35:215-230,2015).In this paper we concentrate our efforts on the PPs of more general form f (x) =(axq + bx + c)r φ((axq + bx + c)(q2-1)/d)+ uxq + vx over Fq2,where a,b,c,u,v ∈ Fq2,r ∈ Z+,φ(x) ∈ Fq2”x”and d is an arbitrary positive divisor of q2-1.The key step is the construction of a commutative diagram with specific properties,which is the basis of the Akbary-Ghioca-Wang (AGW) criterion.By employing the AGW criterion two times,we reduce the problem of determining whether f (x) permutes Fq2 to that of verifying whether two more polynomials permute two subsets of Fq2.AS a consequence,we find a series of simple conditions for f(x) to be a PP of Fq2.These results unify and generalize some known classes of PPs.
Permutation Finite field Commutative diagram AGW criterion
Yanbin Zheng Pingzhi Yuan Dingyi Pei
Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin, Chin School of Mathematics, South China Normal University, Guangzhou, China School of Mathematics and Information Science, Guangzhou University, Guangzhou, China;Key Laboratory
国内会议
桂林
英文
75-91
2017-05-01（万方平台首次上网日期，不代表论文的发表时间）