Permutation polynomials over finite fields - A survey of recent advances

被引：164
作者：
Hou, Xiang-dong [1 ]
机构：
[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2015年 / 32卷
关键词：
Finite field; Permutation polynomial; BINOMIALS; PROOF; TRINOMIALS; CONJECTURE; IDENTITIES; THEOREMS; INVERSE; WELCH;
D O I：
10.1016/j.ffa.2014.10.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Permutation polynomials over finite fields constitute an active research area in which advances are being made constantly. We survey the contributions made to this area in recent years. Emphasis is placed on significant results and novel methods. (C) 2014 Elsevier Inc. All rights reserved.
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页码：82 / 119
页数：38
相关论文
共 94 条
[1]   A generalized lucas sequence and permutation binomials [J].
Akbary, A ;
Wang, Q .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (01) :15-22
[2]  
Akbary A., 2007, Int. J. Math. Math. Sci, V2007, P23408
[3]   On constructing permutations of finite fields [J].
Akbary, Amir ;
Ghioca, Dragos ;
Wang, Qiang .
FINITE FIELDS AND THEIR APPLICATIONS, 2011, 17 (01) :51-67
[4]   On permutation polynomials of prescribed shape [J].
Akbary, Amir ;
Ghioca, Dragos ;
Wang, Qiang .
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (02) :195-206
[5]  
Ball S, 2004, LECT NOTES COMPUT SC, V2948, P79
[6]  
Blokhuis A, 2001, FINITE FIELDS AND APPLICATIONS, P37
[7]  
Brioschi F., 1879, Rend. Reale Ist. Lombardo Sci. Lett. (2), V12, P483
[8]  
Brioschi F., 1870, Math. Ann, V2, P467
[9]   Binary m-sequences with three-valued crosscorrelation:: A proof of Welch's conjecture [J].
Canteaut, A ;
Charpin, P ;
Dobbertin, H .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (01) :4-8
[10]   Constructing permutation polynomials from piecewise permutations [J].
Cao, Xiwang ;
Hu, Lei ;
Zha, Zhengbang .
FINITE FIELDS AND THEIR APPLICATIONS, 2014, 26 :162-174
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