论文标题
几乎完美的线性Lee填料半径2仅适用于小尺寸
Almost perfect linear Lee codes of packing radius 2 only exist for small dimensions
论文作者
论文摘要
大约半个世纪前，Golomb和Welch猜想，没有完美的Lee代码$ C $包装半径$ r $ in $ \ MATHBB {z}^{n} $ for $ r \ geq2 $和$ n \ geq 3 $。最近，Leung和第二作者证明了$ r = 2 $的线性Lee代码的猜想。一个自然的问题是，是否可以将第二好的分类，即几乎完美的线性Lee Radius $ 2 $。我们表明，如果在$ \ mathbb {z}^n $中存在此类代码，则$ n $必须为$ 1,2、11、11、11、29、47、56、67、79、104、121、134 $或$ 191 $。
It is conjectured by Golomb and Welch around half a century ago that there is no perfect Lee codes $C$ of packing radius $r$ in $\mathbb{Z}^{n}$ for $r\geq2$ and $n\geq 3$. Recently, Leung and the second author proved this conjecture for linear Lee codes with $r=2$. A natural question is whether it is possible to classify the second best, i.e., almost perfect linear Lee codes of packing radius $2$. We show that if such codes exist in $\mathbb{Z}^n$, then $n$ must be $1,2, 11, 29, 47, 56, 67, 79, 104, 121, 134$ or $191$.
