The Construction of Two New Series of Two-Weight Codes over Finite Fields

doi:10.3969/j.issn.0372-2112.2019.03.028

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The Construction of Two New Series of Two-Weight Codes over Finite Fields

更新时间：2025-07-02

- The Construction of Two New Series of Two-Weight Codes over Finite Fields
- Acta Electronica Sinica Vol. 47, Issue 3, Pages: 714-718(2019)
- 作者机构：
  
  1. 安徽大学数学科学学院,安徽,合肥,230601
  3. 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
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61672036);Youth Fund of Natural Science Foundation of Anhui Province (No.1808085J20)
- DOI：10.3969/j.issn.0372-2112.2019.03.028
  CLC： TN911.22
- Published Online：25 March 2019，
  
  Published：2019
- 稿件说明：
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The Construction of Two New Series of Two-Weight Codes over Finite Fields[J]. Acta Electronica Sinica, 2019, 47(3): 714-718.
DOI：

The Construction of Two New Series of Two-Weight Codes over Finite Fields[J]. Acta Electronica Sinica, 2019, 47(3): 714-718. DOI： 10.3969/j.issn.0372-2112.2019.03.028.

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

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.

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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