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...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.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 69973034, 60373087, 60673071)
文摘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.
基金supported by NNSF of China (60162060), and the trans-century training program foundation forthe talents by the education ministry of china, and the foundation for university key teascher by theeducation ministry of china
