几种Cayley图上的验证码与定位码  

Identifying and Locating Codes on Some Cayley Graphs

作　　者：鲁启铭 宋淑娇 Lu Qiming;Song Shujiao(School of Mathematics and Information Science,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,烟台264005

出　　处：《数学理论与应用》2024年第1期78-92,共15页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.61771019);山东省自然科学基金项目(No.ZR2020MA044)资助。

摘　　要：2019年,Junnila,Laihonen和Paris研究了循环图C_(n)(1,d),C_(n)(1,d−1,d)和C_(n)(1,d−1,d,d+1)上的定位码和验证码.本文研究p^(2)阶和2n阶交换群上的八度以内的Cayley图的定位码和验证码,确定它们的最优界,并给出达到最优界的码的例子.这推广了多个关于定位码和验证码的结果.In 2019,Junnila,Laihonen and Paris studied the identifying codes and locating codes on the circulant graphs C_(n)(1,d),C_(n)(1,d−1,d)and C_(n)(1,d−1,d,d+1).In this paper we study the identifying codes and locating codes of Cayley graphs on the Abelian groups of order p^(2)and order 2n within 8 degrees,determine their optimal bounds,and give some examples that reach the optimal bounds.Our results generalize multiple results on identifying and locating codes.

关 键 词：验证码 定位码 最优码 密度 

分 类 号：O157.5[理学—数学]