论文标题
$ \ ell_1 $ - metric的最佳代码，恒定重量
Optimal codes with small constant weight in $\ell_1$-metric
论文作者
论文摘要
由实时DNA中的数据存储的重复纠正问题的动机，我们研究了$ \ ell_1 $ - metric的恒定代码的构建。通过在组合设计理论中使用包装和组可分割的设计，我们为所有可能的距离提供了与非阴性整数和最佳三元代码的最佳代码构造和最佳三元代码。通常，我们得出了最大的三元代码的大小，具有恒定重量$ w $和距离$ 2W-2 $，适用于足够大的长度$ n $满足$ n \ equiv 1，w，-w+2，-2w+3 \ pmod {w（w-1）} $。
Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $\ell_1$-metric. By using packings and group divisible designs in combinatorial design theory, we give constructions of optimal codes over non-negative integers and optimal ternary codes with $\ell_1$-weight $w\leq 4$ for all possible distances. In general, we derive the size of the largest ternary code with constant weight $w$ and distance $2w-2$ for sufficiently large length $n$ satisfying $n\equiv 1,w,-w+2,-2w+3\pmod{w(w-1)}$.
