超立方体幂图最大独立集的一个注记  

A Note on the Maximum Independent Set of the Power of Hypercubes

作　　者：吕梦欣 寇永芳 胡晓敏 李玉瑛 杨卫华 

机构地区：[1]太原理工大学数学学院,山西 晋中

出　　处：《应用数学进展》2021年第1期172-179,共8页Advances in Applied Mathematics

摘　　要：编码理论中的一个基本问题是求最小Hamming距离为d的最大n长二元码集的大小,即求超立方体d-1次幂的最大独立集。本文运用构造超立方体d-1次幂最大独立集的方法得到几类特殊的A(n,d)的值:对于,如果,则A(n,d)=2;如果,则A(n,d)=4;如果n=3k,,且,则A(n,d)=4。A basic problem in coding theory is to find the size of the maximum n-length binary code with the minimum Hamming distance d. That can be regarded as the size of the maximum independent set of the (d−1)th power of n-dimensional hypercube. In this paper, we use the method of constructing the maximum independent set of the (d−1)th power of n-dimensional hypercube to obtain several values of A(n,d) for some special n and d: For , if , then A(n,d)=2;if, then A(n,d)=4;if n=3k, , and , then A(n,d)=4.

关 键 词：超立方体 最大独立集 编码理论 码距 

分 类 号：G63[文化科学—教育学]