环F_p[v]/(v^m-v)上线性码的Gray映射及其应用

Gray maps on linear codes over F_p[v]/(v^m-v) and their applications

本文定义了环F_p[v]/(v^m-v)上线性码的Gray映射.该映射具有一般性,是某些特殊Gray映射的推广.利用这种一般的Gray映射,本文定义了环F_p[v]/(v^m-v)上线性码的Gray重量和Gray距离.另外给出了一类特殊的Gray映射,该映射具有保持自对偶性的性质.并在该类的某个映射下,构造了有限域F7上一个新的参数为[16,8,6]的自对偶码.

In this paper, we define the general Gray maps on linear codes over IFp[v]/（v^m - v）, which lead to Gray weights and Gray distances of linear codes. We give a special class of Gray maps, which preserve the property of self-dual of linear codes from the ring Fp[v]/（vm - v） to the finite field Fp. Moreover, a self-dual code [16, 8, 6] with new weight distribution over Fr is obtained by a special Gray map.