论文标题
重量$ w $和距离$ 2W-2 $ in $ \ ell_1 $ metric的最佳三元代码
Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric
论文作者
论文摘要
$ \ ell_1 $ metric中恒定重量代码的研究是由重复纠正的问题用于实时DNA中的数据存储的动机。在给定长度$ n $，重量$ w $，最小距离$ d $和字母尺寸$ q $的情况下，确定代码的最大尺寸很有趣。在本文中，基于图形分解，我们确定了所有足够大的长度$ n $的恒定重量$ W $和距离$ 2W-2 $的三元代码的最大尺寸。以前，这仅以非常稀疏的家庭$ N $密度$ 4/w（W-1）$而闻名。
The study of constant-weight codes in $\ell_1$-metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum size of a code given the length $n$, weight $w$, minimum distance $d$ and the alphabet size $q$. In this paper, based on graph decompositions, we determine the maximum size of ternary codes with constant weight $w$ and distance $2w-2$ for all sufficiently large length $n$. Previously, this was known only for a very sparse family $n$ of density $4/w(w-1)$.
