论文标题
在几何图中具有最低特征值的完全常规代码上
On completely regular codes with minimum eigenvalue in geometric graphs
论文作者
论文摘要
我们证明，任何几何图G中具有最小特征值的任何完全规则的代码对应于G的集团图中的一个完全规则的代码。研究这些代码的相互关系，获得了Johnson Graphs J（N，W）中完全定期的代码，并获得了覆盖Radius W-1和强度1。特别是，该结果完成了Johnson Graphs J（n，3）中完全常规代码的表征。我们还对约翰逊图J（n，4）中的强度1的完全规则代码进行了分类，而特征值只有一个案例。
We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrelation of these codes, a complete characterization of the completely regular codes in the Johnson graphs J(n,w) with covering radius w-1 and strength 1 is obtained. In particular this result finishes a characterization of the completely regular codes in the Johnson graphs J(n,3). We also classify the completely regular codes of strength 1 in the Johnson graphs J(n,4) with only one case for the eigenvalues left open.
