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Univariate and Multivariate Merit Factors

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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

Merit factor of a binary sequence is reviewed, and constructions are described that appear to satisfy an asymptotic merit factor of 6.3421... Multivariate merit factor is characterised and recursive Boolean constructions are presented which satisfy a non-vanishing asymptote in multivariate merit factor. Clifford merit factor is characterised as a generalisation of multivariate merit factor and as a type of quantum merit factor. Recursive Boolean constructions are presented which, however, only satisfy an asymptotic Clifford merit factor of zero. It is demonstrated that Boolean functions obtained via quantum error correcting codes tend to maximise Clifford merit factor. Results are presented as to the distribution of the above merit factors over the set of binary sequences and Boolean functions.

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Authors and Affiliations

  1. The Selmer Center, Department of Informatics, University of Bergen, PB 7800, N-5020, Bergen, Norway

    Matthew G. Parker

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  1. Matthew G. Parker
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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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Parker, M.G. (2005). Univariate and Multivariate Merit Factors. 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_4

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  • DOI: https://doi.org/10.1007/11423461_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26084-4

  • Online ISBN: 978-3-540-32048-7

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