computational complexity

, Volume 1, Issue 3, pp 235–256

Existence and efficient construction of fast Fourier transforms on supersolvable groups

  • Ulrich Baum

DOI: 10.1007/BF01200062

Cite this article as:
Baum, U. Comput Complexity (1991) 1: 235. doi:10.1007/BF01200062


The linear complexityLK(A) of a matrixA over a fieldK is defined as the minimal number of additions, subtractions and scalar multiplications sufficient to evaluateA at a generic input vector. IfG is a finite group andK a field containing a primitive exp(G)-th root of unity,LK(G):= min{LK(A)|A a Fourier transform forKG} is called theK-linear complexity ofG. We show that every supersolvable groupG has amonomial Fourier Transform adapted to a chief series ofG. The proof is constructive and gives rise to an efficient algorithm with running timeO(|G|2log|G|). Moreover, we prove that these Fourier transforms are efficient to evaluate:LK(G)≤8.5|G|log|G| for any supersolvable groupG andLK(G)≤1.5|G|log|G| for any 2-groupG.

Key words

fast Fourier transforms linear complexity supersolvable groups monomial representations 

Subject classifications

20C15 20C40 68Q40 

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Ulrich Baum
    • 1
  1. 1.Institut für InformatikUniversität BonnBonnGERMANY

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