Multi-continued Fraction Algorithm and Generalized B-M Algorithm over F 2

The asymptotic normalized linear complexity of multisequences

“…This form is given for all q, and the calculations are independent of q. Since we are using only the degrees of the partial denominators, not their precise coefficients, and require only the knowledge of = 0 vs. = 0, the BDM as derived from [4] remains valid for all q.…”

“…We start with the mSCFA by Dai et al [3,4]. The m-SCFA can be described in two ways: In [4], the calculations are made on a symbol-by-symbol basis, considering the so-called "discrepancy" (m, n) ∈ F q at every step.…”

“…The m-SCFA can be described in two ways: In [4], the calculations are made on a symbol-by-symbol basis, considering the so-called "discrepancy" (m, n) ∈ F q at every step. It was given only for q = 2 (underlying field F 2 ).…”

Advances in cryptography and information security—introduction of 2002–2006 progress of SKLOIS

“…This approach has also provided a disproof to one of the conjectures made by Xing in 2000. Instead, a new sufficient and necessary condition for judging when a multi-dimensional sequence is d-perfect is given, and a sufficient and necessary condition is given for judging when the conjecture of Xing about the d-perfect property is true [4]. Now our theory about the multi-dimensional fractions has become a fundamental tool in the study of multi-dimensional sequences.…”

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

“…In this paper we study this problem. In the light of multi-continued fraction theories [5][6][7] , we first transform it into a counting problem on multi-strict continued fractions (m-SCFs, in short), and then make a classification and counting for m-SCFs, which are corresponding to multi-sequences of multiplicity m and length n . 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.…”