Decoding Algorithm to Composite Errors Consisting of Deletions and Insertions for Quantum Deletion-Correcting Codes Based on Quantum Reed-Solomon Codes

TL;DR

This paper introduces an efficient decoding algorithm for quantum deletion-correcting codes based on quantum Reed-Solomon codes, specifically addressing composite errors involving deletions and insertions.

Contribution

It provides the first practical decoding algorithm for Hagiwara codes to correct composite deletion and insertion errors.

Findings

Decoding algorithm successfully corrects composite errors in Hagiwara codes.

Enhances the practical applicability of quantum Reed-Solomon based deletion-correcting codes.

Abstract

This paper focuses on Hagiwara codes, which are quantum deletion-correcting codes constructed by the quantum Reed-Solomon codes. Although Hagiwara codes can correct composite errors consisting of deletions and insertions, an efficient decoding algorithm to such errors remains an open problem. In this paper, we provide a decoding algorithm to such errors for Hagiwara codes.