Laced Boolean functions and subset sum problems in finite fields

Authors:
David Canright;Sugata Gangopadhyay;Subhamoy Maitra;Pantelimon Stnic
Affiliations:
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216, USA;Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India;Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700 108, India;Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216, USA
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

In this paper, we investigate some algebraic and combinatorial properties of a special Boolean function on n variables, defined using weighted sums in the residue ring modulo the least prime p=n. We also give further evidence relating to a question raised by Shparlinski regarding this function, by computing accurately the Boolean sensitivity, thus settling the question for prime number values p=n. Finally, we propose a generalization of these functions, which we call laced functions, and compute the weight of one such, for every value of n.