Recently, 9-variable booleanfunctions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation symmetricbooleanfunctions (RSBFs) by ...
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ISBN:
(纸本)9783540772231
Recently, 9-variable booleanfunctions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation symmetricbooleanfunctions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable booleanfunctions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and dihedral symmetric boolean functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, hence they cannot be made balanced easily. This result also shows that the covering radius of the first order Reed-Muller code R(1, 9) is at least 242.
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