| 一类新的二次广义Bent函数 |
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| 引用本文： | 龚心,;高光普,;刘文芬.一类新的二次广义Bent函数[J].信息工程大学学报,2014,15(6):670-677. |
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| 作者姓名： | 龚心 ;高光普 ;刘文芬 |
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| 作者单位： | [1]信息工程大学,河南郑州450001; [2]数学工程与先进计算国家重点实验室,河南郑州450001; [3]洛阳外国语学院,河南洛阳471003 |
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| 摘 要： | Bent函数广泛应用于密码学、编码等领域.利用线性化置换多项式构造了GF（pn）上一类新的二次广义Bent函数kΣi=0Trn1（cixpei＋1）＋σ·Tr1n/2（cm/2xpn/2＋1）,其中,ci∈GF（pe）,n=me,k=「 m/2」-1,σ≡m＋ 1mod 2,并给出了这类函数为广义Bent函数的两个充要条件.针对m=pvhr和m =2pvhr这两种情形,p和h是满足一定条件的奇素数,给出了GF（pn）上二次广义Bent函数kΣi=0Trn1（cixpei＋1）＋σ·Tr1n/2（cm/2xpn/2＋1）的个数.
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| 关 键 词： | 广义Bent函数 线性化多项式 循环矩阵 容斥原理 |
New Generalized Quadratic Bent Functions in Polynomial Forms |
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| Affiliation: | GONG Xin, GAO Guang-pu , LIU Wen-fen (1. Information Engineering University, Zhengzhou 450001, China; 2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China; 3. Luoyang University of Foreign Languages, Luoyang 471003, China) |
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| Abstract: | Bent functions are widely used in the fields of coding theory and cryptography. This paper constructs a class of quadratic generalized bent functions in the form of kΣi=0Trn1（cixpei＋1）＋σ·Tr1n/2（cm/2xpn/2＋1）,wheren=me,k=rm/27-1,σ=--m＋l mod ci∈GF（pe）,n=me,k=「 m/2」-1,σ≡m＋ 1mod 2,by using the theory of linearized polynomial. Moreover, two necessary and sufficient conditions are presented. Then, the enumerations of those functions are also considered for are odd primes. |
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| Keywords: | generalized bent function linearized polynomial circulant matrix inclusion-exclusion principle |
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