List-decodable Codes for Single-deletion Single-substitution with List-size Two

TL;DR

This paper introduces an explicit code construction capable of list-decoding single-deletion and single-substitution errors with a list size of two, achieving lower redundancy than previous explicit codes.

Contribution

The paper provides a new explicit construction of list-decodable codes with reduced redundancy for single-deletion and substitution errors, improving upon prior explicit methods.

Findings

Redundancy of 3log n+4 achieved

Lower redundancy than previous explicit codes

Effective list decoding with list size two

Abstract

In this paper, we present an explicit construction of list-decodable codes for single-deletion and single-substitution with list size two and redundancy 3log n+4, where n is the block length of the code. Our construction has lower redundancy than the best known explicit construction by Gabrys et al. (arXiv 2021), whose redundancy is 4log n+O(1).