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On the matrix feedback shift register synthesis for matrix sequences



In this paper, a generalization of the linear feedback shift register synthesis problem is presented for synthesizing minimum-length matrix feedback shift registers (MFSRs for short) to generate prescribed matrix sequences and so a new complexity measure, that is, matrix complexity, is introduced. This problem is closely related to the minimal partial realization in linear systems and so can be solved through any minimal partial realization algorithm. All minimum-length MFSRs capable of generating a given matrix sequence with finite length are characterized and a necessary and sufficient condition for the uniqueness issue is obtained. Furthermore, the asymptotic behavior of the matrix complexity profile of random vector sequences is determined.



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    利用对偶格的性质, 对于有限长的矩阵序列, 给出了所有生成该序列的最短的矩阵反馈移位寄存器及其唯一的充要条件。

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Correspondence to Liping Wang.

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Wang, L., Zeng, G. On the matrix feedback shift register synthesis for matrix sequences. Sci. China Inf. Sci. 59, 32107 (2016).

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  • Berlekamp-Massey algorithm
  • minimal partial realization
  • multisequences
  • σ-LFSR


  • Berlekamp-Massey 算法
  • 极小部分实现
  • 多重序列
  • σ-LFSR