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

2026-05-12

AI Summary

Although Hagiwara codes are capable of correcting combined deletion and insertion errors, the longstanding absence of an efficient decoding algorithm has hindered their practical deployment. This work presents the first efficient decoding scheme for Hagiwara codes constructed from quantum Reed–Solomon codes. By integrating classical synchronization error correction techniques with the structural properties of quantum codes, the proposed method establishes a decoding framework tailored to quantum deletion–insertion errors. The approach successfully corrects composite synchronization errors, substantially enhancing the practicality and feasibility of Hagiwara codes and addressing a critical gap in efficient decoding for this class of quantum error-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.

Problem

• quantum deletion-correcting codes
• Hagiwara codes
• composite errors
• deletions and insertions
• decoding algorithm

Innovation

• quantum deletion-correcting codes
• Hagiwara codes
• composite errors
• decoding algorithm
• quantum Reed-Solomon codes