关于A(n,d,w)的一个注记

A Note on A(n,d,w)

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,则;当3≤d≤4时,有 或。

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-1th 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 .