Generalized rotation symmetric and dihedral symmetric boolean functions - 9 variable boolean functions with nonlinearity 242


Kavut S., Yucel M. D.

17th International Symposium on Applied Algebra, Algebrais Algorithms and Error-Correcting Codes, Bangalore, Hindistan, 16 - 20 Aralık 2007, cilt.4851, ss.321-329 identifier identifier

  • Cilt numarası: 4851
  • Basıldığı Şehir: Bangalore
  • Basıldığı Ülke: Hindistan
  • Sayfa Sayıları: ss.321-329

Özet

Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable Boolean functions 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.