Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes
Yixuan Xie, Jinhong Yuan, Yuichiro Fujiwara
TL;DR
This paper introduces a new method for constructing quantum synchronizable codes using quadratic residue codes and their supercodes, achieving optimal synchronization capabilities for cyclic codes of prime length.
Contribution
It presents a simple construction method for quantum synchronizable codes from quadratic residue codes, reaching the upper bound of synchronization capabilities.
Findings
Constructed quantum synchronizable codes with optimal synchronization.
Applicable to cyclic codes of prime length.
Method simplifies existing code construction processes.
Abstract
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes that satisfy special properties, only a few classes of cyclic codes have been proved to give promising quantum synchronizable codes. In this paper, using quadratic residue codes and their supercodes, we give a simple construction for quantum synchronizable codes whose synchronization capabilities attain the upper bound. The method is applicable to cyclic codes of prime length.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography