有限域上两类线性码的构造  

Constructions of two families of linear codes over finite fields

作　　者：李文婷 衡子灵 李晓茹 Li Wenting;Heng Ziling;Li Xiaoru(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《河南师范大学学报（自然科学版）》2024年第3期98-105,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12271059,11901049);陕西省高校科协青年人才托举计划项目(20200505);长安大学中央高校基本科研业务费专项资金(300102122202).

摘　　要：利用定义集的方法构造了两类p元线性码,研究了它们的参数和重量分布.第一类线性码为三重极小码,可用于构造具有安全高效访问结构上的密钥共享方案.第二类线性码为二重线性码,且当p=3时为自正交射影码,可用于构造量子码和强正则图.Two families of linear codes are constructed based on the defining-set method.The parameters and weight distributions of the codes are studied.The first family of linear codes have three weights and are minimal.They can be used to construct secret sharing schemes with interesting access structures.The second family of linear codes have two weights.If p=3,they are projective and self-orthogonal codes which can be used to construct strongly regular graphs and quantum codes.

关 键 词：线性码 自正交码 极小码 重量分布 

分 类 号：O236.2[理学—运筹学与控制论]