Optimal Constant-Weight Codes under $l_1$-Metric

Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $l_1$-metric. By combinatorial methods, we give constructions of optimal ternary codes with $l_1$-weight $w\leq 4$ for all possible distances. In general, we determine the maximum size of ternary codes with constant weight $w$ and distance $2w-2$ for sufficiently large length under certain conditions.