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Sequences from Cocycles

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

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Abstract

Binary and quaternary sequences with perfect periodic autocorrelation, and perfect nonlinear p m-ary sequences, are both shown to equate to orthogonal coboundaries — the simplest class of orthogonal cocycles. We consider doubly-indexed sequences defined by cocycles. We give a new construction — a generalised multiplication — of orthogonal cocycles and show it gives perfect nonlinear sequences for parameters where 1-dimensional PN sequences cannot exist.

This work was supported by Australian Research Council Grant A49701206.

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Author information

Authors and Affiliations

  1. RMIT University, Melbourne, VIC, 3001, Australia

    Kathy J. Horadam

Authors
  1. Kathy J. Horadam
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Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Horadam, K.J. (1999). Sequences from Cocycles. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_12

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  • DOI: https://doi.org/10.1007/3-540-46796-3_12

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  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

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