Self-dual bent functions
Self-dual bent functions
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DOI：
10.1504/ijicot.2010.032864
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
C. Carlet;Lars Eirik Danielsen;M. Parker;P. Solé
中科院分区：
文献类型：
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作者：
C. Carlet;Lars Eirik Danielsen;M. Parker;P. Solé
一个bent函数被称为自对偶，如果它等于它的对偶。如果它等于它的对偶的补，则称为反自对偶。推导出了用西尔维斯特阿达玛矩阵的瑞利商表示的谱特征。给出了奇数元布尔函数的Rayleigh商的界。基于西尔维斯特矩阵的谱，提出了一种有效的搜索算法.主要和次要的结构。给出了所有≤ 6元的自对偶Bent布尔函数和所有8元的二次Bent布尔函数，直到仿射等价的限制形式。
A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterisation in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of the Sylvester matrix is derived. Primary and secondary constructions are given. All self-dual bent Boolean functions in ≤ 6 variables and all quadratic such functions in eight variables are given, up to a restricted form of affine equivalence.