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Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property
Authors: Subhamoy MaitraAbstract:
Constructing highly nonlinear balanced Boolean functions with very good
autocorrelation property is an interesting open question. In this direction
we use the measure \Delta_f for a function f proposed by Zhang and
Zheng (1995). We provide balanced functions f with currently best known
nonlinearity and \Delta_f values together. Our results for 15-variable
functions disprove the conjecture proposed by Zhang and Zheng (1995),
where our constructions are based on modifications of
Patterson-Wiedemann (1983) functions. Also we propose a simple
bent based construction technique to get functions with very good
\Delta_f values for odd number of variables. This construction has
a root in Kerdock Codes. Moreover, our construction on even number
of variables is a recursive one and we conjecture (similar to Dobbertin’s
conjecture (1994) with respect to nonlinearity) that this provides
minimum possible value of \Delta_f for a function f on even number
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