Classification and counting on multi-continued fractions and its application to multi-sequences.

*(English)*Zbl 1142.40001Summary: In the light of multi-continued fraction theories, we make a classification and counting for multi-strict continued fractions, which are corresponding to multi-sequences of multiplicity \(m\) and length \(n\). Based on the above counting, we develop an iterative formula for computing fast the linear complexity distribution of multi-sequences. As an application, we obtain the linear complexity distributions and expectations of multi-sequences of any given length \(n\) and multiplicity \(m\) less than 12 by a personal computer. But only results of \(m=3\) and 4 are given in this paper.

##### MSC:

40A15 | Convergence and divergence of continued fractions |

40B05 | Multiple sequences and series (should also be assigned at least one other classification number in this section) |

94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |

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\textit{Z. Dai} and \textit{X. Feng}, Sci. China, Ser. F 50, No. 3, 351--358 (2007; Zbl 1142.40001)

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##### References:

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