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Multi-continued fraction algorithm and generalized B-M algorithm over $$F_{2}$$. (English) Zbl 1145.94413
Helleseth, T. (ed.) et al., Sequences and their applications – SETA 2004. Third international conference, Seoul, Korea, October 24–28, 2004. Revised selected papers. Berlin: Springer (ISBN 978-3-540-26084-4/pbk). Lecture Notes in Computer Science 3486, 339-354 (2005).
Summary: It is shown that the generalized Berlekamp-Massey algorithm (GBMA, in short) for solving the linear synthesis problem of a multi-sequence $$\underline r$$ over $$F_{2}$$ can be obtained naturally from a special form of the multi-continued fraction algorithm, called the multi-strict continued fraction algorithm (m-SCFA, in short). Moreover, the discrepancy sequence in acting GBMA on $$\underline r$$ is expressed explicitly by the data associated to the multi-strict continued fraction expansion $$C(\underline r)$$ which is obtained by applying m-SCFA on $$\underline r$$. As a consequence, a 1-1 correspondence between multi-sequences of any given length and certain multi-strict continued fractions is established.
For the entire collection see [Zbl 1131.94003].

##### MSC:
 94A55 Shift register sequences and sequences over finite alphabets in information and communication theory 94A60 Cryptography 11A55 Continued fractions 11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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