• DocumentCode
    985286
  • Title

    A Counterexample to a Conjecture of Niho

  • Author

    Langevin, Philippe ; Leander, Gregor ; McGuire, Gary

  • Author_Institution
    GRIM-USTV, Univ. of Toulon, La Garde
  • Volume
    53
  • Issue
    12
  • fYear
    2007
  • Firstpage
    4785
  • Lastpage
    4786
  • Abstract
    A conjecture of Niho states that under certain assumptions the Fourier transform of the function Tr (xd) on F2n ,where d = (2tk1) /(2k +1), has a spectrum with at most five values. We present a counterexample to this conjecture, and the theory behind finding it. We use the theory of quadratic forms over F2.
  • Keywords
    Fourier transforms; Walsh functions; Fourier transform; Niho states conjecture; quadratic forms theory; spectrum; Boolean functions; Fourier transforms; Galois fields; Gold; Polarization; Terminology; 5-valued; Fourier; Walsh; quadratic form; spectrum;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2007.909109
  • Filename
    4385773
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=985286