On the Maximum Number of Non-Confusable Strings Evolving under Short Tandem Duplications

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