糾兩個錯的二元戈帕碼的完全譯碼算法
AN ALGORITHM OF COMPLETE DECODING OF DOUBLE-ERROR-CORRECTING GOPPA CODES
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摘要: 本文給出生成多項式G(z)=z2+z+、具有參數(shù)(2m,2m-2m,5)的糾兩個錯的二元戈帕(Goppa)碼完全譯碼的一個算法。這個算法最多只需要m次計算GF(2)上m維向量的內積和解GF(2m)上二次方程的根,就可實現(xiàn)完全譯碼。對m12,本文的算法已在IBM-PC機上實現(xiàn)。
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關鍵詞:
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]馮貴良,電子科學學刊,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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