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- W85188401 abstract "Let m,q > 1 be two integers that are co-prime and A be any subset of Zm. Let P be any multi-variate polynomial of degree d in n variables over Zm. We show that the MODq boolean function on n variables has correlation at most exp( (n/(m2 m 1 ) d )) with the boolean function f defined by f(x) = 1 iff P(x) 2 A for all x 2 {0,1} n . This improves on the bound of exp( (n/(m2 m ) d )) obtained in the breakthrough work of Bourgain [3] and Green et al. [9]. Our calculation is also slightly shorter than theirs. Our result immediately implies the bound of exp( (n/4 d )) for the special case of m = 2. This bound was first reported in the recent work of Viola [11]. [11] states that it is not clear how to extend their method to general m." @default.
- W85188401 created "2016-06-24" @default.
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- W85188401 date "2006-01-01" @default.
- W85188401 modified "2023-09-23" @default.
- W85188401 title "An improved bound on correlation between polynomials over Z_m and MOD_q." @default.
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