### 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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionsBinary StringCounting
Contact author(s)
yuanli7983 @ gmail com
History
2010-02-27: last of 3 revisions
See all versions
Short URL
https://ia.cr/2009/554

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},
note = {\url{https://eprint.iacr.org/2009/554}},
url = {https://eprint.iacr.org/2009/554}
}

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