Laced Boolean functions and subset sum problems in finite fields

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.