Construction of high degree resilient S-boxes with improved nonlinearity

We present a simple method to use an [n−d−1,m,t+1] code to construct an n-input, m-output, t-resilient function with degree d>m and nonlinearity 2n−1−2n−⌈(d+1)/2⌉−(m+1)2n−d−1. For any fixed values of parameters n,m,t and d, with d>m, the nonlinearity obtained by our construction is higher than the nonlinearity obtained by Cheon in Crypto 2001.