Cryptology ePrint Archive: Report 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.

Category / Keywords: Boolean functions, Binary String, Counting

Date: received 12 Nov 2009, last revised 27 Feb 2010

Contact author: yuanli7983 at gmail com

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Version: 20100227:173652 (All versions of this report)

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