标题： 在$\ell_1$-度量下的具有小常数重量的最优码 显示英文标题

标题： Optimal codes with small constant weight in $\ell_1$-metric

摘要： 受用于实时DNA数据存储的复制纠正问题的启发，我们研究了$\ell_1$度量下等重码的构造。 通过组合设计理论中的覆盖和分组可除设计，我们给出了非负整数上的最优码和具有$\ell_1$权$w\leq 4$的最优三元码的构造，适用于所有可能的距离。 一般来说，我们推导出在足够长的长度$n$满足$n\equiv 1,w,-w+2,-2w+3\pmod{w(w-1)}$时，具有常权$w$和距离$2w-2$的最大三元码的大小。 显示英文摘要

摘要： 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 $n\equiv 1,w,-w+2,-2w+3\pmod{w(w-1)}$.