On asymmetric error-correcting codes

R. R. Varshamov

Jos H. Weber

Ji Fan

Since Calderbank et al.established CRSS construction,which constructs quantum error-correcting codes(QECC) from classical error-correcting codes,many QECC demonstrating good performance have been constructed from classical error-correcting codes;these codes are referred to as quantum stabilizer codes.Recent physical experiments indicate that the probabilities of occurrence of qubit-flip errors are much less than those of phase-flip errors in most quantum mechanical systems.Error-correcting codes thus constructed are referred to as asymmetric quantum codes.In this paper,series of asymmetric quantum stabilizer codes are constructed using nested Goppa codes and dual contained Goppa codes.In the construction of asymmetric quantum codes based on nested Goppa codes,the choice of Goppa codes is limited to construct codes with analysis methods.In normal circumstances,the construction is executed with the help of mathematical software Matlab,which is used to compute the minimum distance of Goppa codes.In the construction of asymmetric quantum codes based on dual contained Goppa codes,the error correction ability of the codes constructed in this paper is reflected in the correction of Z-type errors.

James L. Massey

Yue RAN, Juan XU, Hanwu Chen +2 more

Since Calderbank et al. established CRSS construction, which constructs quantum error-correcting codes (QECC) from classical error-correcting codes, many QECC demonstrating good performance have been constructed from classical error-correcting codes; these codes are referred to as quantum stabilizer codes. Recent physical experiments indicate that the probabilities of occurrence of qubit- ip errors are much less than those of phase- ip errors in most quantum mechanical systems. Error-correcting codes thus constructed are referred to as asymmetric quantum codes. In this paper, series of asymmetric quantum stabilizer codes are constructed using nested Goppa codes and dual contained Goppa codes. In the construction of asymmetric quantum codes based on nested Goppa codes, the choice of Goppa codes is limited to construct codes with analysis methods. In normal circumstances, the construction is executed with the help of mathematical software Matlab, which is used to compute the minimum distance of Goppa codes. In the construction of asymmetric quantum codes based on dual contained Goppa codes, the error correction ability of the codes constructed in this paper is re ected in the correction of Z-type errors

W. W. Peterson