超立方体幂图中常重点集导出子图的一类独立集  

A Class of Independent Sets of Subgraphs Derived from Constant Focus Sets in Hypercube Power Graphs

作　　者：师娟娟 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》2022年第3期1170-1177,共8页Advances in Applied Mathematics

摘　　要：编码理论中的一个基本问题是求A(n,d,w)的值,即长度为n,重量为w,最小Hamming距离为d的二元码集的大小。它可看作是n维超立方体 次幂图中所有重量为w的点导出子图Qn(d-1,w)的最大独立集。本文运用构造图Qn(d-1,w)的最大独立集的方法得到n、d和w为某些特殊值时,A(n,d,w)=4 。A basic problem in coding theory is to find the value of A(n,d,w), that is, the size of the maximum binary code with length n, constant weight w and minimum Hamming distance d. It can also be re-garded as the maximum independent set of induced subgraph of points of weight w of the th d-1th-power of n-dimensional hypercube Qn(d-1,w) . We use the method of constructing the maximum independent set of Qn(d-1,w) to obtain A(n,d,w)=4 for some special n, d and w.

关 键 词：超立方体 最大独立集 常重码 

分 类 号：O157.5[理学—数学]