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QUATERNARY DELSARTE-GOETHALS AND GOETHALS-DELSARTE CODES

QUATERNARY DELSARTE-GOETHALS AND GOETHALS-DELSARTE CODES
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摘要 In this paper, the quaternary Delsarte-Goethals code D(m,δ) and its dual code G(m,δ) are discussed. The type and the trace representation are given for D(m,δ), while the type and the minimum Lee weight are determined for G(m,δ). The shortened codes of D(m,δ) and G(m,δ) are proved to be 4-cyclic. The binary image of D(m,δ) is proved to be the binary Delsarte-Goethals code DG(m+1,δ),and the essential difference between the binary image of G(m,δ) and the binary Goethals-Delsarte codeGD(m+1,δ) is exhibited. Finally, the decoding algorithms of D■(m,δ) and G(m,δ) are discussed.
出处 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2002年第1期43-51,共9页 系统科学与复杂性学报(英文版)
关键词 Quaternary Delsarte-Goethals code quaternaryGoethals-Delsarte code. 整数环 四元Delsarte-Gothols码 四元Goethals-Delsarte码
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参考文献5

  • 1A. R. Hammon, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane: and R Sole, The 2Z4-linearity of Kerdock, Preparers, Goethals, and related codes, IEEE Transations on Information Theory, 1994,40:301-319.
  • 2Zhe-Xian Wan: The Quaternary Codes, World Scientific, Singapore, 1997.
  • 3P. Delsarte and J. M. Goethals, Alternating bilinear forms over GF(q), Journal of Combinatorial Theory, Serieo A, 1975, 19: 26-59.
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  • 5T. Helleseth, and P. V. Kumar, The algebraic decoding of the 2Z4-linear Goethals code, IEEE Transations on Information Theory, 1995, 41: 2040-2048.

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