Constructing Quantum Error-Correcting Codes for pm-State Systems from Classical Error-Correcting Codes

Ryutaroh MATSUMOTO  Tomohiko UYEMATSU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.10   pp.1878-1883
Publication Date: 2000/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
quantum codes,  stabilizer codes,  additive codes,  self-orthogonal codes,  

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We generalize the construction of quantum error-correcting codes from F4-linear codes by Calderbank et al. to pm-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of quantum codes with efficient decoding algorithms.