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Classification and counting on multi-continued fractions and its application to multi-sequences. (English) Zbl 1142.40001
Summary: 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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