Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes

摘要

Quantum synchronizable codes are quantum error-correcting codes designed tocorrect the effects of both quantum noise and block synchronization errors.While it is known that quantum synchronizable codes can be constructed fromcyclic codes that satisfy special properties, only a few classes of cycliccodes have been proved to give promising quantum synchronizable codes. In thispaper, using quadratic residue codes and their supercodes, we give a simpleconstruction for quantum synchronizable codes whose synchronizationcapabilities attain the upper bound. The method is applicable to cyclic codesof prime length.