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The study of constant-weight codes in $\ell_1$-metric was motivated by theduplication-correcting problem for data storage in live DNA. It is interestingto 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 graphdecompositions, we determine the maximum size of ternary codes with constantweight $w$ and distance $2w-2$ for all sufficiently large length $n$.Previously, this was known only for a very sparse family $n$ of density$4/w(w-1)$.

Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric