The non-adaptive query complexity of testing k-parities
  We prove tight bounds of Theta(k log k) queries for non-adaptively testing whether a function f:{0,1}^n -> {0,1} is a k-parity or far from any k-parity. The lower bound combines a recent method of Blais, Brody and Matulef [BBM11] to get lower bounds for testing from communication complexity with an Omega(k \log k) lower bound for the one-way communication complexity of k-disjointness. 
Harry Buhrman, David Garcia-Soriano, Arie Matsliah, and Ronald de Wolf
cs.CC cs.DS