Des. Codes Cryptogr. DOI 10.1007/s10623-012-9740-0 Towards the classification of self-dual bent functions in eight variables Thomas Feulner · Lin Sok · Patrick Solé · Alfred Wassermann Received: 28 September 2011 / Revised: 10 August 2012 / Accepted: 11 August 2012 © Springer Science+Business Media, LLC 2012 Abstract In this paper, we classify quadratic and cubic self-dual bent functions in eight variables with the help of computers. There are exactly four and 45 non-equivalent self-dual bent functions of degree two and three, respectively. This result is achieved by enumerating all eigenvectors with ±1 entries of the Sylvester Hadamard matrix with an integer programming algorithm based on lattice basis reduction. The search space has been reduced by breaking the symmetry of the problem with the help of additional constraints. The final number of non- isomorphic self-dual bent functions has been determined by exploiting that EA-equivalence of Boolean functions is related to the equivalence of linear codes. Keywords Boolean functions · Bent functions · Integer programming · EA-equivalence Mathematics Subject Classification (2000) 06E30 · 65T50 · 94A60 This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”. T. Feulner · A. Wassermann (B ) Mathematical Department, University of Bayreuth, Bayreuth 95440, Germany e-mail: alfred.wassermann@uni-bayreuth.de T. Feulner e-mail: thomas.feulner@uni-bayreuth.de L. Sok · P. Solé Department Comelec, Telecom ParisTech, 46, rue Barrault, Paris 75013, France e-mail: sok@telecom-paristech.fr P. Solé MECAA, Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia e-mail: sole@telecom-paristech.fr 123