| 摘要: |
| 同时达到代数次数上界n-m-1和非线性度上界2n-1-2m+1的n元m阶弹性布尔函数(m＞n/2-2)具有3个Walsh谱值:0,±2m+2这样的函数被称为饱和最优函数(saturated best,简称SB).将利用(32,6)Reed-Muller码陪集重量的分布,从一种全新的构造角度出发,给出n=5的饱和最优函数的个数. |
| 关键词: 非线性度 相关免疫 Walsh谱 最优函数 |
| DOI： |
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| 基金项目:Supported bythe National Natural Science Foundation of China under Grant No.19931010(国家自然科学基金);the NationalGrand Fundamental Research 973 Program ofChina under GrantNo.G1999035804(国家重点基础研究发展规划(973)) |
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| On the Number of 5-Variable Best Boolean Functions |
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XIE Min,PEI Ding-Yi
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| Abstract: |
| The n-variable and m-resilient (m>n/2-2) Boolean functions achieving both the upper bound on nonlinearity2n-1-2m+1and the upper bound on algebraic degree n-m-1 must have three valued Walsh spectra: 0,±2m+2,which are called saturated best (SB in short). Using the known results of weight distributions of the cosets of the (32,6) Reed-Muller code and a new construction method for SB functions gives the number of the 5-variable SB functions. |
| Key words: nonlinearity correlation immunity Walsh transform best function |
