Please use this identifier to cite or link to this item: https://doi.org/10.1109/TIT.2013.2259138
 Title: All the stabilizer codes of distance 3 Authors: Yu, S. Bierbrauer, J.Dong, Y.Chen, Q. Oh, C.H. Keywords: 1-error correcting stabilizer codesoptimal codesquantum error correctionquantum Hamming bound Issue Date: 2013 Citation: Yu, S., Bierbrauer, J., Dong, Y., Chen, Q., Oh, C.H. (2013). All the stabilizer codes of distance 3. IEEE Transactions on Information Theory 59 (8) : 5179-5185. ScholarBank@NUS Repository. https://doi.org/10.1109/TIT.2013.2259138 Abstract: We give necessary and sufficient conditions for the existence of stabilizer codes [[n,k,3]] of distance 3 for qubits: n-k [log 2(3n+1)] +\epsilon n, where n=1 if n=8 4m-1 3+± 1,2\ or n= 4m+2-1 3-1,2,3 for some integer m 1 and n=0 otherwise. Or equivalently, a code [[n,n-r,3]] exists if and only if n (4r-1)/3 (4r-1)/3-n\notin \lbrace 1,2,3\rbrace for even r and n 8(4 r-3-1)/3, 8(4r-3-1)/3-n\ne 1 for odd r. Given an arbitrary length n, we present an explicit construction for an optimal quantum stabilizer code of distance 3 that saturates the above bound. © 1963-2012 IEEE. Source Title: IEEE Transactions on Information Theory URI: http://scholarbank.nus.edu.sg/handle/10635/116215 ISSN: 00189448 DOI: 10.1109/TIT.2013.2259138 Appears in Collections: Staff Publications

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