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| 摘要: |
| 本文研究了指数和S(α,β)=Σx∈Fpmχ(αx(pk+1)/(2))+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k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. |
| 关键词: 指数和 循环码 重量分布 二次型 |
| DOI： |
| 分类号:O157.4 |
| 基金项目:Supported by National Natural Science Foundation of China (61379004) and the Postgraduate Innovation Project of Jiangsu Province (KYZZ15-0360). |
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| A CLASS OF THREE-WEIGHT CYCLIC CODES |
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LIANG Hua,CHEN Wen-bing,TANG Yuan-sheng
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| Abstract: |
| In this paper, the value distribution of the exponential sum S(α,β)=Σx∈Fpmχ(αx(pk+1)/(2)+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. |
| Key words: exponential sum cyclic code weight distribution quadratic form |
