| 有限域上两类新的2-重量码的构造 |
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| 引用本文： | 管玥,施敏加,张欣,伍文婷.有限域上两类新的2-重量码的构造[J].电子学报,2019,47(3):714-718. |
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| 作者姓名： | 管玥 施敏加 张欣 伍文婷 |
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| 作者单位： | 安徽大学数学科学学院,安徽合肥,230601;安徽大学数学科学学院,安徽合肥230601;安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039 |
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| 基金项目： | 国家自然科学基金;安徽省自然科学基金 |
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| 摘 要： | 有限域上二重量码的构造是图论、编码与密码中的重要研究课题.本文得到了有限域上两类新的2-重量码并且它们都是最优的，达到了Griesmer界.这些码由有限域的扩域上迹码的p元像定义，有阿贝尔码的代数结构，利用特征和和高斯和来计算了它们的重量分布.我们也计算了这些像码的对偶码的极小距离.最后对扩域上迹码的像在秘钥共享方案中的应用进行了刻画.
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| 关 键 词： | 2-重量码 迹码 循环码 高斯和 秘钥共享方案 Griesmer界 |
| 收稿时间： | 2018-02-19 |
The Construction of Two New Series of Two-Weight Codes over Finite Fields |
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| GUAN Yue,SHI Min-jia,ZHANG Xin,WU Wen-ting.The Construction of Two New Series of Two-Weight Codes over Finite Fields[J].Acta Electronica Sinica,2019,47(3):714-718. |
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| Authors: | GUAN Yue SHI Min-jia ZHANG Xin WU Wen-ting |
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| Affiliation: | 1. School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China;
2. Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei, Anhui 230039, China |
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| Abstract: | The construction of two-weight codes over finite fields is an important research topic in graph,coding and cryptography fields.We obtain two new series of two-weight codes over finite fields and they are both optimal,which arrive at Griesmer bound.These codes are defined as p-ary images of trace codes over the extended fields.They have the algebraic structure of abelian codes.Their weight distributions are evaluated explicitly by using character sums,Gauss sums in particular.We also calculate the minimum distance of the dual codes of the image codes.Finally,an application of the Gray images of trace codes over the extended fields to secret sharing schemes is described. |
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| Keywords: | two-weight codes trace codes cyclic codes Gauss sums secret sharing schemes Griesmer bound |
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