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

【摘要】 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.更多还原

【Abstract】 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.更多还原