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This paper presents a construction for a class of 1-resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying the generating matrix. For n is small (e.g. n = 6), a part of these functions achieve almost optimal nonlinearity. Apart from their good nonlinearity, the functions reach Siegenthaler's  upper bound ofdoi:10.1007/s11390-011-9433-6 fatcat:wixo5sppdrfnjdt77rzyi5gbd4