Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE COMPUTATION OF THE NON-PERIODIC AUTOCORRELATION FUNCTION OF TWO TERNARY SEQUENCES AND ITS RELATED COMPLEXITY ANALYSIS

  • Koukouvinos, Christos (Department of Mathematics, National Technical University of Athens) ;
  • Simos, Dimitris E. (Department of Mathematics, National Technical University of Athens)
  • Received : 2010.06.27
  • Accepted : 2010.10.28
  • Published : 2011.05.30
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Abstract

We establish a new formalism of the non-periodic autocorrelation function (NPAF) of two sequences, which is suitable for the computation of the NPAF of any two sequences. It is shown, that this encoding of NPAF is efficient for sequences of small weight. In particular, the check for two sequences of length n having weight w to have zero NPAF can be decided in $O(n+w^2{\log}w)$. For n > w^2{\log}w$, the complexity is O(n) thus we cannot expect asymptotically faster algorithms.

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