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In a recent paper Zhang-Xiao, Zhang and Xiao describe a technique on constructing almost optimal resilient functions on even number of variables. In this paper, we will present an extensive study of the constructions of almost optimal resilient functions by using the generalized Maiorana-McFarland (GMM) construction technique. It is shown that for any given m, it is possible to construct infinitely many n-variable (n even), m-resilient Boolean functions with nonlinearity equal toarXiv:1003.3492v1 fatcat:okszokdf7nh3rm3gw7mrobbaji