Analysis of affinely equivalent Boolean functions  

作　　者：MENG QingShu ZHANG HuanGuo YANG Min WANG ZhangYi 

机构地区：[1]Computer School, Wuhan University, Wuhan 430074, China [2]State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430074, China [3]International School of Software, Wuhan University, Wuhan 430074, China

出　　处：《Science in China(Series F)》2007年第3期299-306,共8页中国科学（F辑英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 69973034, 60373087, 60673071)

摘　　要：By some basic transforms and invariant theory, we give two results： 1） an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2） Reed-Muller codes R（4,6）/R（1,6）, R（3,7）/R（1,7） are classified efficiently.By some basic transforms and invariant theory, we give two results： 1） an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2） Reed-Muller codes R（4,6）/R（1,6）, R（3,7）/R（1,7） are classified efficiently.

关 键 词：Boolean functions Reed-Muller code affinely equivalent INVARIANT 

分 类 号：O153.2[理学—数学]