关于覆盖半径为$ρ=1$的线性完全正则码入级与建造
On linear completely regular codes with covering radius $ρ=1$. Construction and classification
摘要：
具有覆盖半径$ρ=1$的完全正则码必须具有最小距离$d\leq 3$。对于$d=3$，这样的码是完美的，并且它们的参数是公知的。本文研究了$d=1$和$d=2$的情形，并在码是线性的情况下完全刻画了这两种情形.此外，还证明了所有这些码都是完全传递的。
英文摘要：
Completely regular codes with covering radius $ρ=1$ must have minimum distance $d\leq 3$. For $d=3$, such codes are perfect and their parameters are well known. In this paper, the cases $d=1$ and $d=2$ are studied and completely characterized when the codes are linear. Moreover, it is proven that all these codes are completely transitive.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
