Generalized Gray map and a class of p-ary nonlinear codes

In this paper, we investigate a generalized Gray map G   on ZpkZpk with p a prime, which generalizes a Carlet's result in [1]. For a ZpkZpk-valued function f(x)f(x), we use exponential sums to express the Hamming weight of G(f(x))G(f(x)). As an application, a family of nonlinear codes over FpFp is obtained from the generalized Gray map. We use the Weil-type exponential sums over Galois rings to provide a lower bound for the minimum distance of these codes.