基于二次乘法特征的射影线性码  

Projective Linear Codes Based on the Quadratic Multiplicative Characters

作　　者：陈辅灵 衡子灵 王鑫然 李成举 CHEN Fu-ling;HENG Zi-ling;WANG Xin-ran;LI Cheng-ju(School of Science,Chang'an University,Xi'an,Shaanxi 710064,China;State Key Laboratory of Mobile Communication,Southeast University,Nanjing,Jiangsu 210096,China;Key Laboratory of Highly Trusted Computing,East China Normal University,Shanghai 200062,China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]东南大学移动通信国家重点实验室,江苏南京210096 [3]华东师范大学高可信计算重点实验室,上海200062

出　　处：《电子学报》2023年第1期32-41,共10页Acta Electronica Sinica

基　　金：国家自然科学基金(No.11901049,No.12071138);陕西省高校科协青年人才托举计划(No.20200505);东南大学移动通信国家重点实验室开放研究基金(No.2022D05);长安大学中央高校基本科研业务费专项资金(No.300102122202);上海市可信工业互联网软件协同创新中心项目。

摘　　要：基于有限域上的二次乘法特征构造了两类线性码,精确计算出了它们的参数和重量分布.结果表明,第一类线性码是射影三重码,且对偶码关于球填充界几乎最优;第二类线性码是射影二重码,且对偶码关于球填充界几乎最优.此外,本文还得到了一些自正交码和极小码,它们可分别用于构造量子码和安全高效访问结构上的密钥共享方案.Two families of linear codes are constructed based on the quadratic multiplicative characters of finite fields. The parameters and weight distributions of the codes are explicitly determined. It turns out that the first family of linear codes are projective three-weight ones whose duals are almost optimal according to the sphere-packing bound. The second family of linear codes are projective two-weight ones whose duals are also almost optimal according to the sphere-packing bound. Besides, some self-orthogonal codes and minimal codes are obtained. The self-orthogonal codes can be used to construct quantum codes and minimal codes can be used to construct secret sharing schemes with safe and sufficient access structures.

关 键 词：射影码 增信码 自正交码 极小码 

分 类 号：O236.2[理学—运筹学与控制论]