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

In this paper, we investigate a generalized Gray map G on Z p k with p a prime, which generalizes a Carlet's result in 1. For a Z p k -valued function f ( x ) , we use exponential sums to express the Hamming weight of G ( f ( x ) ) . As an application, a family of nonlinear codes over F p 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.

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