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《电子学报(英文)》 2018-05
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The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions

DU Jiao;FU Shaojing;QU Longjiang;LI Chao;PANG Shanqi;College of Mathematics and Information Science,Henan Normal University;Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University;College of Computer Science,National University of Defense Technology;College of Liberal Arts and Science,National University of Defense Technology;  
A new characterization of balanced rotation symmetric(n, m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric(p~r, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric(2~r, m)-functions for 2 ≤ m ≤ 2~r-r. With the help of these results, we also prove that there exist rotation symmetric resilient(2~r, m)-functions for 2 ≤ m ≤ 2~r-r-1.
【Fund】: supported by National Key R&D Program of China(No.2017YFB0802000);; National Natural Science Foundation of China(No.61672530 No.61722213 No.61572026 No.U1404601 No.11501181);; Ph.D research startup foundation of Henan Normal University(No.5101019170133)
【CateGory Index】: TN918.1
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