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On the symmetric property of homogeneous boolean functions

Chapter


Abstract


  • We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V6. We found two interesting classes of degree 3 homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second is degree 3 homogeneous balanced boolean functions. Both the bent and balanced functions discovered have nice algebraic and combinatorial structures. We note that some structures can be extended to a large boolean space. The application of homogeneous boolean functions for fast implementation on parallel architectures is mooted.

Publication Date


  • 1999

Citation


  • Qu, C., Seberry, J., & Pieprzyk, J. (1999). On the symmetric property of homogeneous boolean functions. In Unknown Book (Vol. 1587, pp. 26-35). doi:10.1007/3-540-48970-3_3

International Standard Book Number (isbn) 13


  • 9783540657569

Scopus Eid


  • 2-s2.0-84885903924

Web Of Science Accession Number


Book Title


  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Start Page


  • 26

End Page


  • 35

Abstract


  • We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V6. We found two interesting classes of degree 3 homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second is degree 3 homogeneous balanced boolean functions. Both the bent and balanced functions discovered have nice algebraic and combinatorial structures. We note that some structures can be extended to a large boolean space. The application of homogeneous boolean functions for fast implementation on parallel architectures is mooted.

Publication Date


  • 1999

Citation


  • Qu, C., Seberry, J., & Pieprzyk, J. (1999). On the symmetric property of homogeneous boolean functions. In Unknown Book (Vol. 1587, pp. 26-35). doi:10.1007/3-540-48970-3_3

International Standard Book Number (isbn) 13


  • 9783540657569

Scopus Eid


  • 2-s2.0-84885903924

Web Of Science Accession Number


Book Title


  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Start Page


  • 26

End Page


  • 35