纠两个错的二元戈帕码的完全译码算法
AN ALGORITHM OF COMPLETE DECODING OF DOUBLE-ERROR-CORRECTING GOPPA CODES
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摘要: 本文给出生成多项式G(z)=z2+z+、具有参数(2m,2m-2m,5)的纠两个错的二元戈帕(Goppa)码完全译码的一个算法。这个算法最多只需要m次计算GF(2)上m维向量的内积和解GF(2m)上二次方程的根,就可实现完全译码。对m12,本文的算法已在IBM-PC机上实现。
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Abstract: In this paper an algorithm of complete decoding procedure for the Goppa codes with generator polynomial G(z)=z2+z+ and parameters (2m, 2m-2m, 5) is shown. The algorithm requires at most m times calculatng inner product of vectors over GF(2) and finding roots of quadratic equation in GF(2m). Por m 12, the algorithm has been realized. -
F. J. Macwiilians, and N. J, A. Sloane, The Theory of Error-Correcting Codes, North-Holland,1977.[2]D. C. Gotenstein, W W Peterson and N. Zierlet, Infor. and Control, 3(1960), 291-4.[3]C. R. P. Hartmann, IEEE Trans. on IT, IT-17(1971), 765-6.[4]冯贵良,电子科学学刊,5(1983), 343-8.[5]O. Moreno, Goppa Codes Related Quasi-Perfe-t Double-Error-Correcting Codes, Presented at IEEE Int. Symposium on Information Theory, Santa Monica, U. S, A., 1981.[6]G. L. Feng and K. K. Tzeng, On Quasi-Perfect Property of Double-Error-Correcting Goppa Codes and Their Complete Decoding, Presented at IEEE Int. Symposium on Information Theory, St. Jovite, Quebic, Canada, 1983.[7]C. L. Chen, IEEE Trans. on IT, IT-28(1982), 792-4. -
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