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Volume 19 Issue 2
Mar.  1997
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Yue Dianwu, Hu Zhengming. ALGEBRAIC DECODING OF GOPPA CODES FROM A POLYNOMIAL IDEAL POINT OF VIEW[J]. Journal of Electronics & Information Technology, 1997, 19(2): 274-277.
Citation: Yue Dianwu, Hu Zhengming. ALGEBRAIC DECODING OF GOPPA CODES FROM A POLYNOMIAL IDEAL POINT OF VIEW[J]. Journal of Electronics & Information Technology, 1997, 19(2): 274-277.

ALGEBRAIC DECODING OF GOPPA CODES FROM A POLYNOMIAL IDEAL POINT OF VIEW

  • Received Date: 1995-03-13
  • Rev Recd Date: 1995-06-30
  • Publish Date: 1997-03-19
  • Prom a polynomial ideal point of view, a general algebraic method for decoding Goppa codes is presented. It is shown that such a method can correct t = [(d - 1)/2] errors, where d is the true minimum distance of the given Goppa code.
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  • Brinton Cooper III A. Direct solution of BCH decoding equations, Communication, Control and Signal Processing. Amsterdam, The Netherlands Elsevier Science Publishers, 1990, 281-286.[2]Chen X, et al. Use of Grobner bases to decode binary cyclic codes up to the true minimum distance. IEEE Trans. on IT., 1994, IT-40(5): 1654-1660.[3]Chen X, et al. General principles for the algebraic decoding of cyclic codes. IEEE Trans. on IT.,1994, IT-40(5): 1661-1663.[4]MacWilliams F J, Sloane N J A. The theory of error-correcting codes, Amsterdam: North Holland Pubiahers, 1977.[5]Massey J L. Shift-register synthesis and BCH decoding. IEEE Trans. on IT., 1969, IT-15(1): 122- 127.[6]岳殿武.求分圆陪集首元的新算法.通信保密,1995, 16(1): 28-32.[7]岳殿武循环陪集结构及其应用.系统科学与数学,1992, 12(1): 15-20.[8]Lang S. Algebra, 2nd ed. Memo Park, CA: Addison-Wesley, 1984, 375.[9]Buchberger B. Grobner Bases: An Algorithmic Method in Polynomial Ideal Theory, Multidimensional Systems Theory. Dordrecht: Reidel, 1985, 185-232.[10]Becker T. Grobner Basea. NewYork: Springer-Verlag, 1993.[11]冯贵良,曾开明.广义Goppa码最小距离下限的扩张及其译码,中国科学,1983, 12.(8): 745-755.
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