A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by t...A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by the prime number, and more disks can be dynamically appended in a running storage system. L codes can tolerate at least two disk erasures and some sector loss simultaneously, and can tolerate multiple disk erasures（greater than or equal to three） under a certain condition. Because only XOR operations are needed in the process of encoding and decoding, L codes have very high computing efficiency which is roughly equivalent to X codes. Analysis shows that L codes are particularly suitable for large-scale storage systems.展开更多
We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal c...We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61202250
文摘A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by the prime number, and more disks can be dynamically appended in a running storage system. L codes can tolerate at least two disk erasures and some sector loss simultaneously, and can tolerate multiple disk erasures（greater than or equal to three） under a certain condition. Because only XOR operations are needed in the process of encoding and decoding, L codes have very high computing efficiency which is roughly equivalent to X codes. Analysis shows that L codes are particularly suitable for large-scale storage systems.
文摘We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.
