We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum error...We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.展开更多
An isomorphism preserving Hamming distance between two algebraic geometry(AG)codes is presented to obtain the main parameters of Justesen’s algebraic geometry(JAG)codes.To deduce a simple approach to the decoding alg...An isomorphism preserving Hamming distance between two algebraic geometry(AG)codes is presented to obtain the main parameters of Justesen’s algebraic geometry(JAG)codes.To deduce a simple approach to the decoding algorithm,a code word in a“small”JAG codeis used to correspond to error-locator polynomial.By this means,a simple decoding procedureand its ability of error correcting are explored obviously.The lower and upper bounds of thedimension of AG codes are also obtained.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.61170321the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20110092110024the Scientific Research Innovation Plan for College Graduates of Jiangsu Province under Grant No.CXZZ13 0105
文摘We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.
文摘An isomorphism preserving Hamming distance between two algebraic geometry(AG)codes is presented to obtain the main parameters of Justesen’s algebraic geometry(JAG)codes.To deduce a simple approach to the decoding algorithm,a code word in a“small”JAG codeis used to correspond to error-locator polynomial.By this means,a simple decoding procedureand its ability of error correcting are explored obviously.The lower and upper bounds of thedimension of AG codes are also obtained.
