Assume we have two strings $S_1$ and $S_2$ of lengths $cn$ and $cm$ bits resepctively for some $c\in\Bbb N$.Assume that the Levenshtein distance (minimum number of single-character edits (i.e. insertions, deletions or substitutions)) between $S_1$ and $S_2$ over binary alphabet is $L(2)$.For any $b$ such that $b>1$ and $b|c$ consider the strings $S_1$ and $S_2$ over alphabet $\{0,1,\dots,2^b-1\}$. Assume the Levenshtein distance between $S_1$ and $S_2$ over $b$-ary alphabet is $L(2^b)$.Is there any relation between $L(2)$ and $L(2^b)$ in general?Can we say anything for LCS (minimum number of insertions or deletions) distance as well?
Relation between edit distances over different alphabets
edit distance