Optimal codes in deletion and insertion metric

TL;DR

This paper improves the upper bound on the size of single-deletion correcting codes of length 4 over even-sized alphabets and constructs an optimal perfect code achieving this bound.

Contribution

It provides a tighter upper bound for such codes and presents a construction of an optimal perfect code, advancing coding theory for deletion errors.

Findings

New upper bound matches the constructed code, proving optimality.

Constructed code is perfect and corrects single deletions.

The bound is sharp, confirming its tightness.

Abstract

We improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an optimal perfect code capable of correcting single deletions for the same parameters.