  The set of all $ q $-ary strings that do not contain repeated substrings of
length $ \leqslant\! 3 $ (i.e., that do not contain substrings of the form $ a
a $, $ a b a b $, and $ a b c a b c $) constitutes a code correcting an
arbitrary number of tandem-duplication mutations of length $ \leqslant\! 3 $.
In other words, any two such strings are non-confusable in the sense that they
cannot produce the same string while evolving under tandem duplications of
length $ \leqslant\! 3 $. We demonstrate that this code is asymptotically
optimal in terms of rate, meaning that it represents the largest set of
non-confusable strings up to subexponential factors. This result settles the
zero-error capacity problem for the last remaining case of tandem-duplication
channels satisfying the "root-uniqueness" property.
