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QUANTUM CODES CONSTRUCTED FROM BINARY CYCLIC CODES

Department of Computer Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710016, People's Republic of China

Department of Applied Mathematics and Physics, College of Art and Science, Air Force Engineering University, Xi'an, Shaanxi 710053, People's Republic of China

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and

XUELIANG LI

Center for Combinatorics, Nankai University, Tianjin 300071, People's Republic of China

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https://doi.org/10.1142/S0219749904000213Cited by:24 (Source: Crossref)

Abstract

In this paper, we use 2-cyclotomic cosets of modulo n and generator polynomials to describe binary cyclic codes of length N=2^αn with n odd. We discuss the conditions under which two cyclic codes and can be used to construct quantum codes by CSS construction or Steane's construction. Using the results of Chen, Promhouse and Tavares, and Castagnoli et al., we study the quantum codes that can be constructed from binary cyclic codes of length N=2^αn with n odd and n≤99, and α≤2. We find that except the quantum codes constructed by Steane, there are also some very interesting quantum codes constructed from repeated-root cyclic codes, and some of the quantum codes constructed by Steane can be improved.

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