基于有限域上射影码的t-设计和强正则图  

Combinatorial t-designs and Strongly Regular Graphs from Projective Codes over Finite Fields

作　　者：衡子灵 李德祥 王啸 Zi Ling HENG;De Xiang LI;Xiao WANG(School of Science,Chang'an University,Xi'an 710064,P.R.China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《数学学报（中文版）》2024年第1期195-208,共14页Acta Mathematica Sinica：Chinese Series

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资助项目(20200505);长安大学中央高校基本科研业务费专项资金资助项目(300102122202)。

摘　　要：有限域上射影码在组合设计和强正则图中有重要应用.本文首先构造一类二元线性码并在四种情形下研究其参数和重量分布,结果表明这类线性码是射影码且在两种情形下是最优码,它们的对偶码关于球填充界最优或几乎最优;然后利用这些射影码构造t-设计和强正则图.Projective codes over finite fields have important applications in combina-torial designs and strongly regular graphs.In this paper,we first construct a family of linear codes and then study their parameters and weight distributions in four cases.It turns out that the proposed linear codes are projective and are optimal in two cases.The duals of these codes are either optimal or almost optimal according to the sphere-packing bound.As applications,these codes are used to construct t-designs and strongly regular graphs.

关 键 词：线性码 T-设计 强正则图 

分 类 号：O236.2[理学—运筹学与控制论]