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, India, 16 - 20 December 2007, vol.4851, pp.321-329 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 4851
  • City: Bangalore
  • Country: India
  • Page Numbers: pp.321-329
  • Keywords: rotation symmetric boolean functions, dihedral symmetric boolean functions, nonlinearity, REED-MULLER CODES, COVERING RADIUS, COSETS, IMMUNITY, ORPHANS, WEIGHT, BENT
  • Middle East Technical University Affiliated: Yes


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.