Algebraic techniques in designing quantum synchronizable codes
Yuichiro Fujiwara, Vladimir D. Tonchev, Tony W. H. Wong
TL;DR
This paper enhances the design of quantum synchronizable codes by leveraging finite field theory, expanding error tolerance, and introducing new code families based on Reed-Muller codes.
Contribution
It improves the general framework for quantum synchronizable codes and provides algebraic insights and new code constructions using finite fields and Reed-Muller codes.
Findings
Wider range of tolerable synchronization errors
New families of quantum synchronizable codes based on Reed-Muller codes
Deeper algebraic understanding of synchronization recovery
Abstract
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.
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