Algebraic techniques in designing quantum synchronizable codes

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.

9 pages, no figures. The framework presented in this article supersedes the one given in arXiv:1206.0260 by the first author

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Cited by in corpus (10)

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• Parsing a sequence of qubits
• Quantum Block and Synchronizable Codes Derived from Certain Classes of Polynomials
• Quantum Synchronizable Codes on Sextic Cyclotomy
• Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes
• A new family of quantum synchronizable codes from negacyclic codes
• Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over ${\mathbb{Z}}_{2q}$
• The Asymptotics of Difference Systems of Sets for Synchronization and Phase Detection
• Algebraic Quantum Synchronizable Codes
• Two New Families of Quantum Synchronizable Codes