摘要:
编码理论中的一个基本问题是求A(n,d,w)的值，即最小Hamming距离为d的最大n长二元常重码集的大小。而A(n,d,w)又可看作是n维超立方体d-1次幂图中所有重量为w的点导出子图
的最大独立集。故为探索
的最大独立集，本文首次给出了图
的定义，对其一些基本性质进行了研究并得到如下主要结果：
是
-正则图；是点传递图；对于2≤d≤3，若w≥[n/2]，则
；若
w<[n/2]，则
；当
3≤d≤4时，有
或
。
Abstract:
A basic problem in coding theory is to find the value of
A(n,d,w), that is the size of the maximum n-length binary constant weight code with the minimum Hamming distance d. However, it can be regarded as the size of the maximum independent set of
which is a subgraph of d-1
th power of n-dimensional hypercube induced by all vertices with constant weight w. To explore the maximum independent set of
, this paper gives the definition of
for the first time. Furthermore, some basic properties of the graph are studied and the main results are obtained as follows:
is
-regular.
is vertex transitive. For
2≤d≤3, if
w≥[n/2], then
; if , then . For
3≤d≤4,
or
.