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Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with Respect to the {I,H,N}n Transform

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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

We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR IHN , peak-to-average power ratio with respect to the {I,H,N}n transform set. We prove that PAR IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR IHN and algebraic degree higher than 2.

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Authors and Affiliations

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

    Lars Eirik Danielsen & Matthew G. Parker

Authors
  1. Lars Eirik Danielsen
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  2. 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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© 2005 Springer-Verlag Berlin Heidelberg

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Danielsen, L.E., Parker, M.G. (2005). Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with Respect to the {I,H,N}n Transform. 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_28

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  • DOI: https://doi.org/10.1007/11423461_28

  • 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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