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Towards the classification of self-dual bent functions in eight variables

Title data

Feulner, Thomas ; Sok, Lin ; Solé, Patrick ; Wassermann, Alfred:
Towards the classification of self-dual bent functions in eight variables.
In: Designs, Codes and Cryptography. Vol. 68 (2013) Issue 1–3 . - pp. 395-406.
ISSN 0925-1022
DOI: https://doi.org/10.1007/s10623-012-9740-0

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
No informationWA-1666/7-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Boolean functions; Bent functions; Integer programming; EA-equivalence
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Jan 2015 10:18
Last Modified: 04 Feb 2015 09:01
URI: https://eref.uni-bayreuth.de/id/eprint/5855