Synthesis of liner feedback shift register allowing give pairs of input and output arrays

本研究的目的是通过扩展我们在代数几何码（AG）快速译码方面的研究成果，开发一种有效的算法来解决允许给定输入输出阵列对的线性反馈移位寄存器的合成问题。该问题是合成能够产生给定输出阵列的线性反馈寄存器问题的延伸，它与RS码、BCH码以及下一代纠错码AG码等实用代数码的快速译码方法密切相关。该问题处理的是非齐次Toeplitz方程和块状Toeplitz方程及其多维扩展，而前者处理的是齐次Toeplitz方程和块状Toeplitz方程及其多维扩展。我们的问题在线性系统理论领域被称为维纳-霍普方程。作为我们的研究成果，我们给出了一种有效的方法来解决我们的问题，更多的一维输入和输出阵列，并在2000年6月30日至7月5日在瑞士洛桑举行的IEEE 2002年信息理论国际研讨会上发表了我们的成果。接下来，我们明确了我们的方法可以应用于在AG码的列表解码第二阶段的多项式在代数函数域上的列表解码第二阶段的多项式的快速因式分解，并分别在2003年6月25日至28日在Awakamogawa举行的第三届亚欧信息论研讨会和2003年6月29日至7月4日在横滨举行的IEEE 2003国际信息论研讨会上发表了这些结果。在本研究开始时，我们从系统论的角度着手解决这个问题，成功地证明了我们的方法可以应用于RS码和AG码的快速列表解码，这是我们提高解码效率的目标之一。与此相关，我们发表了AG码和复合纠错码的并行译码，分别发表在IEICE电子通信与计算机科学基础学报，J85-A, 4,460 -470, 2002（日文）和E86-A， 7,1813 -1819, 2003（英文）。少

The objective of this research is to develop an efficient algorithm for solving the problem of synthesizing linear feedback shift register allowing given pairs of input and output arrays by expanding our research results on fast decoding of algebraic geometric (AG) codes. The problem is an extension of the problem of synthesizing linear feedback shit register capable of generating given output arrays, which is closely related to fast decoding methods of practical algebraic codes such as RS codes, BCH codes and next-generation error-correcting codes, i.e. AG codes. The present problem treats nonhomogeneous Toeplitz and block-Toeplitz equations and their multidimensional extensions, while the former problem treats homogeneous Toeplitz and block-Toeplitz equations and their multidimensional extensions. Our problem is known as Wiener-Hoph equations in the field of linear system theory. As an outcome of our research, we have given an efficient method of solving our problem in case of pairs … More of one-dimensional input and output arrays, and presented our result in the IEEE 2002 International Symposium on Information Theory, in Lausanne, Switzerland, Jun 30-July 5,2000. Next, we have made clear that our method can be applied to fast factorization of polynomials over rational function field in the second stage of list decoding of polynomials over algebraic function field in the second stage of list decoding of AG codes, and presented these results in the Third Asian-European Workshop on Information Theory, in Awakamogawa, Jun 25-28, 2003, and in the IEEE 2003 International Symposium on Information Theory, in Yokohama, Jun 29-July 4, 2003, respectively. In the beginning of this research we undertook to solve the problem from a standpoint of system theory so that we have succeeded to show that our method can be applied to fast list decoding of RS codes and AG codes, which was one of our aims for more efficient decoding method. Related to the research, we published papers on parallel decoding of AG codes and compound-error-correcting codes in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, J85-A, 4, 460-470, 2002 (in Japanese), and E86-A, 7, 1813-1819, 2003 (in English). Less