Linear List Decodable Edit-Correcting Codes with Rate Approaching $1$

TL;DR

This paper introduces linear edit-correcting codes with rates approaching 1, capable of correcting edits with polynomial-time encoding and decoding, surpassing previous limits for deletion-correcting codes.

Contribution

It constructs linear list decodable codes with high rate approaching 1 that can correct edits efficiently, improving upon the known rate bounds for deletion-correcting codes.

Findings

Codes with rate approaching 1 are achievable for edit correction.

The codes are linear, list decodable, and have polynomial-time algorithms.

They can correct a broad class of edits with manageable list sizes.

Abstract

Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.