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

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

2005-04-25

arxiv.org/abs/cs/0504102v1

In Sequences and Their Applications -- SETA 2004, edited by T. Helleseth, D. Sarwate, H.-Y. Song, and K. Yang, Lecture Notes i

Computer Science

Information Theory

Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figures

Scientific paper

10.1007/11423461_28

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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