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

作者：Heng, Ziling; Yue, Qin^*

来源：Finite Fields and Their Applications, 2015, 36: 81-97.

DOI：10.1016/j.ffa.2015.06.006

• Gray map
• Galios rings
• Exponential sums

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.

• 出版日期2015-11
• 单位南京航空航天大学