A Search Algorithm for Bases of Calderbank-Shor-Steane Type Quantum Error-Correcting Codes

Kin-ichiroh TOKIWA  Hatsukazu TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.3   pp.860-865
Publication Date: 2001/03/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
quantum error-correcting codes,  CSS codes,  basis,  linear codes,  computer search,  

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Recently, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the Calderbank-Shor-Steane code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. In this paper, we investigate the revised versions given by Vatan et al., and point out that there is no essential difference between them. In addition, we propose an efficient algorithm for searching for bases of quantum error-correcting codes. The proposed algorithm is based on some fundamental properties of classical linear codes, and has much lower complexity than Vatan et al.'s procedure.