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The Solutions of the Third Power Sum Equation for Niho Type Decimations

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3857))

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Abstract

We will completely describe the solutions of the equation (x + 1)d = x d + 1 in the field GF(q 2), where q = p k and d is of Niho type, i.e., d ≡ 1 (mod q − 1). Our results have applications in the theory of cross-correlation functions of m-sequences and in the theory of cyclic codes.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Kalle Ranto & Petri Rosendahl

Authors
  1. Kalle Ranto
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  2. Petri Rosendahl
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, Honolulu, USA

    Marc P. C. Fossorier

  2. National Institute of Advanced Industrial Science and Technology (AIST), Research Center for Information Security (RCIS),  

    Hideki Imai

  3. Department of Electrical and Computer Engineering, University of California, CA 95616, Davis,  

    Shu Lin

  4. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

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© 2006 Springer-Verlag Berlin Heidelberg

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Ranto, K., Rosendahl, P. (2006). The Solutions of the Third Power Sum Equation for Niho Type Decimations. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_9

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  • DOI: https://doi.org/10.1007/11617983_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31423-3

  • Online ISBN: 978-3-540-31424-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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