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

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Sequences and Their Applications - SETA 2004 (SETA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3486))

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Abstract

It is shown that the generalized Berlekamp-Massey algorithm (GBMA, in short) for solving the linear synthesis problem of a multi-sequence 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 r is expressed explicitly by the data associated to the multi-strict continued fraction expansion C( r ) which is obtained by applying m-SCFA on r. As a consequence, a 1-1 correspondence between multi-sequences of any given length and certain multi-strict continued fractions is established.

This work is partly supported by NSFC (Grant No. 60173016), and the National 973 Project (Grant No. 1999035804).

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Authors and Affiliations

  1. State Key Lab of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, 100049, China

    Zongduo Dai & Xiutao Feng

  2. Software Institute, Chinese Academy of Sciences, Beijing, 100049, China

    Junhui Yang

Authors
  1. Zongduo Dai
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  2. Xiutao Feng
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  3. Junhui Yang
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  2. University of Ilinois at Urbana-Champaign, 1406 West Green Street, IL 61801, Urbana, USA

    Dilip Sarwate

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2005 Springer-Verlag Berlin Heidelberg

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Dai, Z., Feng, X., Yang, J. (2005). Multi-continued Fraction Algorithm and Generalized B-M Algorithm over F 2 . In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_25

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  • DOI: https://doi.org/10.1007/11423461_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26084-4

  • Online ISBN: 978-3-540-32048-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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