中文摘要：

本文研究了指数和S（α,β）=∑xx∈Fpm（αx^（p^k＋1）/2）x＋βx^p3k＋1/2））的值分布.应用S（α,β）的值分布,确定了一类p元循环码的重量分布,证明了所提出的循环码具有三个非零重量,这里p是奇素数,m和南是两个正整数,满足m/gcd（m,k）是奇数,k/gcd（m,k）是偶数以及m≥3.

英文摘要：

In this paper,the value distribution of the exponential sum S（α,β）=∑xx∈Fpm（αx^（p^k＋1）/2）x＋βx^p3k＋1/2）） is investigated.Applying the value distribution of S（α,β）,the weight distribution of a class of p-ary cyclic codes is determined.It turns out that the proposed cyclic codes has three nonzero weights,here p is an odd prime,m and k are two positive integers such that m/gcd（m,k） is odd,k = /gcd（m,k） is even and m ≥ 3.