Perfect Multi Deletion Codes Achieve the Asymptotic Optimality of Code Size

TL;DR

This paper investigates the maximum size of perfect multi deletion binary codes, establishing lower bounds and demonstrating the asymptotic optimality of Levenshtein's upper bound for fixed code length and deletions.

Contribution

It provides new bounds and confirms the asymptotic optimality of existing upper bounds for perfect multi deletion codes.

Findings

Established lower bounds for perfect multi deletion codes

Demonstrated asymptotic achievability of Levenshtein's upper bound

Confirmed optimality of code size in the asymptotic regime

Abstract

This paper studies on the cardinality of perfect multi deletion binary codes. The lower bound for any perfect deletion code with the fixed code length and the number of deletions, and the asymptotic achievable of Levenshtein's upper bound are shown.