一类新的二次广义Bent函数  

New Generalized Quadratic Bent Functions in Polynomial Forms

作　　者：龚心 高光普 刘文芬[1,2] 

机构地区：[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

出　　处：《信息工程大学学报》2014年第6期670-677,共8页Journal of Information Engineering University

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∑ki=0Trn1(cixpei+1)+σ·Trn/21(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∑ki=0Trn1(cixpei+1)+σ·Trn/21(cm/2xpn/2+1)的个数。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.

关 键 词：广义BENT函数 线性化多项式 循环矩阵 容斥原理 

分 类 号：TN918[电子电信—通信与信息系统]