An Optimal Tester for k-Linear.

A Boolean function f:{0,1}n→{0,1} is k-linear if it returns the sum (over the binary field F2) of exactly k coordinates of the input. In this paper, we study property testing of the classes k-Linear, the class of all k-linear functions, and k-Linear⁎, the class ∪j=0kj-Linear. We give a non-adaptive distribution-free two-sided ϵ-tester for k-Linear that makesO(klog⁡k+1ϵ) queries. This matches the lower bound known from the literature.