有限域上逻辑函数的退化性  

Degenerate Property of Logical Functions over Finite Fields

作　　者：滕吉红[1] 黄晓英[1] 曾本胜[1] 

机构地区：[1]信息工程大学理学院,河南郑州450001

出　　处：《信息工程大学学报》2010年第2期152-155,共4页Journal of Information Engineering University

摘　　要：首先举例说明素域上逻辑函数退化性的相关结论并不能直接推广到一般有限域上,进一步讨论了一般有限域上逻辑函数的退化性与线性结构的关系。结果表明有限域上逻辑函数的退化性虽然和其0类线性结构之集U(f0)中的元素个数没有直接关系,但可以通过U(f0)中所含的线性子空间的维数来判别逻辑函数的退化程度。The paper firstly verifies that the conclusions about the degenerate property of Boolean function and logical functions over prime fields can not be generalized to that of logical functions over finite fields.Then the relationship between the degenerate property and the linear structure is proposed.Results show that although there is no directly relation between the degenerate property and the number of the elements in the set U（0）f,the degenerate degree of logical functions can still be decided through the dimension of the subspace included in U（0）f,which holds in the case of prime fields.

关 键 词：逻辑函数 退化性 代数免疫 线性结构 Chrestenson谱支集 

分 类 号：O157.4[理学—数学]