多個(gè)序列綜合問題的新模型及其應(yīng)用
SYNTHESIS OF MULTISEQUENCES AND THEIR APPLICATIONS
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摘要: 本文提出新的數(shù)學(xué)模型,用來刻劃序列的綜合問題,并將其推廣,揭示了可用Grbner基理論解決序列的綜合問題,并得到有效的算法,從而成功地開辟了解決多個(gè)序列綜合問題的新途經(jīng).本文另一重要結(jié)果是給出了J.Justesen等構(gòu)造的一類代數(shù)幾何碼(JAG碼)的有效譯碼算法,此算法是Euclid算法的非平凡推廣.Abstract: A new mathematical model, the linear homogeneous equations with polynomial coefficients for describing the synthesis problem, is presented in this paper. It gives a nature approach ro generalize the linear synthesis to nonlinear case. This method is used ro obtain a new solution for the multisequence synthesis. The Grbner bases theory in polynomial ring is used to present an efficient algorithm for the mathematical model. This turns out to be a generalization of Euclid algorithm. However, the new one has much brilliant prospects. As one of the important results, it is discovered that the new algorithm can be used to deduce an efficient decoding algorithm for a class of algebraic geometry codes constructed by Justesen, so the important open problem is solved.
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馮貴良等,中國(guó)科學(xué),A輯,1985年,第8期,第1-12頁.[2]J. Justesen et al., IEEE Trans. on IT, IT-35(1989)4, 811-821.[3]A. N. Skorolwgatov et al., IEEE Trans. on IT, IT-36(1990)5, 1051-1061.[4]O. Zariski, Commutative Algebra II, Springer-Verlag, New York, (1960), pp 192-250.[5]B. Buchberger, Grbner Bases:[6]An Algorithmic Method in Polynomial Ideal Theory, in Multidimensional[7]Systems Theory, Ed. by N. K. Bose, Springer-Verlag, Berlin, (1984), pp. 184-232.[8]H. Moller, J. Algebsa, 100(1986), 138-178.[9]S. Sakata, IEEE Trans. on IT, IT-37(1991)4, 1200-1203. -
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