It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
This study proposes a new explanation for the formation of precipitation anomaly patterns in the boreal summer during the E1 Nifio-Southem Oscillation （ENSO） developing and decaying phases. During the boreal sum- me...This study proposes a new explanation for the formation of precipitation anomaly patterns in the boreal summer during the E1 Nifio-Southem Oscillation （ENSO） developing and decaying phases. During the boreal sum- mer June-July-August （JJA） （0） of the E1 Nino （La Nina） developing phase, the upper level （300-100 hPa） positive potential temperature anomalies resemble a Ma- tsuno-Gill-type response to central Pacific heating （cool- ing）, and the lower level （1000-850 hPa） potential tem- perature anomalies are consistent with local SST anoma- lies. During the boreal summer JJA（1） of the E1 Nifio （La Nifia） decaying phase, the upper level potential tempera- ture warms over the entire tropical zone and resembles a Matsuno-Gill-type response to Indian Ocean heating （cooling）, and the lower level potential temperature anomalies follow local SST anomalies. The vertical heterogeneity of potential temperature anomalies influences the atmospheric stability, which in turn influences the precipitation anomaly pattern. The results of numerical experiments confirm our observations.展开更多
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
基金supported by the National Basic Research Program of China (2006CB400503)the National Natural Science Foundation of China (40890155,40775051,and U0733002)Project KZCX2-YW-220 of the Chinese Academy of Sciences
文摘This study proposes a new explanation for the formation of precipitation anomaly patterns in the boreal summer during the E1 Nifio-Southem Oscillation （ENSO） developing and decaying phases. During the boreal sum- mer June-July-August （JJA） （0） of the E1 Nino （La Nina） developing phase, the upper level （300-100 hPa） positive potential temperature anomalies resemble a Ma- tsuno-Gill-type response to central Pacific heating （cool- ing）, and the lower level （1000-850 hPa） potential tem- perature anomalies are consistent with local SST anoma- lies. During the boreal summer JJA（1） of the E1 Nifio （La Nifia） decaying phase, the upper level potential tempera- ture warms over the entire tropical zone and resembles a Matsuno-Gill-type response to Indian Ocean heating （cooling）, and the lower level potential temperature anomalies follow local SST anomalies. The vertical heterogeneity of potential temperature anomalies influences the atmospheric stability, which in turn influences the precipitation anomaly pattern. The results of numerical experiments confirm our observations.
