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| Analysis of affinely equivalent Boolean functions | |
| 作者单位： | MENG QingShu（Computer School, Wuhan University, Wuhan 430074, China） ; ZHANG HuanGuo（Computer School, Wuhan University, Wuhan 430074, China;State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430074, China） ; YANG Min（International School of Software, Wuhan University, Wuhan 430074, China） ; WANG ZhangYi（Computer School, Wuhan University, Wuhan 430074, China） ; |
| 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. |
Analysis of affinely equivalent Boolean functions |
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| Authors: | Meng QingShu Zhang HuanGuo Yang Min Wang ZhangYi |
| Affiliation: | 1. Computer School, Wuhan University, Wuhan 430074, China 2. Computer School, Wuhan University, Wuhan 430074, China;State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430074, China 3. International School of Software, Wuhan University, Wuhan 430074, China |
| Abstract: | 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. |
| Keywords: | Boolean functions Reed-Muller code affinely equivalent invariant |
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