基于环F4+uF4上的线性码

摘要

The linear codes over F4 + uF4 are studied. By means of a representation of the elements in FA + uF4 and F4 + uF4 to be a Frobenius ring, it is obtained that the Gray images of self-dual codes over F4 + uF4 are also self-dual codes ,and the Gray images of cyclic codes over F4 + uF4 are quasi-cyclic codes. The results of the Gray images of the linear codes over F4 + uFA are extended.%本文研究了环F4+uF4上线性码的Gray像.利用环F4+uF4为Frobenius环及其元素的一种表示方法,获得了环F4+uF4上自对偶码的Gray像也为自对偶码,及环F4+uF4上循环码的Gray像为拟循环码,推广了环F4+uF4上线性码的Gray像的相关结果.