ON A COMBINATORIAL CONJECTURE

T.  W.  CUSICK; YUAN LI; PANTELIMON STANICA

Paper 2009/554

ON A COMBINATORIAL CONJECTURE

T. W. CUSICK, YUAN LI, and PANTELIMON STANICA

Abstract

Recently, Tu and Deng proposed a combinatorial conjecture on binary string, on the premise that the conjecture is correct they obtain two classes of Boolean functions which are both algebraic immunity optimal: the first class of functions are also bent. The second class are balanced functions, which have optimal algebraic degree and the best nonlinearity up to now. In this paper, from three different sides, we prove this conjecture is true in many cases with different counting strategies. We also propose some problems about the weight equations which is related to this conjecture. Because of the scattered distribution, we predict that a general counting is difficult to obtain.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean functions Binary String Counting
Contact author(s): yuanli7983 @ gmail com
History: 2010-02-27: last of 3 revisions; 2009-11-18: received; See all versions
Short URL: https://ia.cr/2009/554
License: CC BY

BibTeX

@misc{cryptoeprint:2009/554,
      author = {T.  W.  CUSICK and YUAN LI and PANTELIMON STANICA},
      title = {{ON} A {COMBINATORIAL} {CONJECTURE}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/554},
      year = {2009},
      url = {https://eprint.iacr.org/2009/554}
}