A new family of quantum synchronizable codes from negacyclic codes

• URL: http://arxiv.org/abs/2107.02648v3
• Date: Fri, 18 Mar 2022 14:11:40 GMT
• Title: A new family of quantum synchronizable codes from negacyclic codes
• Authors: Tao Wang and Tongjiang Yan and Shiwen Sun
• Abstract summary: We propose a new method for construct quantum synchronizable codes from negacyclic codes. This paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.
• Score: 4.3702562340580755
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are $p$ and $pq$. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.

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