The Eigenfunction of the Reed-Muller Transformation

Abstract

We introduce eigenfunctions of the Reed-Muller transform. Eigenfunctions are functions whose canonical sumof- products expression and PPRM (positive polarity Reed- Muller expression) are isomorphic. In the case of symmetric functions, the eigenfunction can be viewed as a function whose reduced truth vector is identical to the reduced Reed- Muller spectrum. We show that the number of symmetric (ordinary) eigenfunctions on n-variables is 2 (n+1 divided by 2) (2 (2n-1)). We identify three special symmetric functions that correspond to the most complicated minimal fixed polarity Reed- Muller (FPRM) form. We show how the transeunt triangle can be used to convert between the reduced (ordinary) truth vector and the reduced (ordinary) Reed-Muller spectrum. We derive the number of products in the FPRM for these symmetric functions: this shows that they have the most complicated minimal FPRM among all n-variable functions.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2007
Accession Number
ADA604853

Entities

People

  • J. T. Bulter
  • T. Sasao

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Algebra
  • Coefficients
  • Computer Science
  • Eigenvectors
  • Equations
  • Infinite Series
  • Information Operations
  • Linear Algebra
  • Mathematics
  • Matrices (Mathematics)
  • National Security
  • Polarity
  • Scientific Research
  • Simultaneous Equations
  • Spectra
  • Triangles
  • Vector Spaces

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  • Calculus or Mathematical Analysis
  • Computer Programming and Software Development.
  • Graph Algorithms and Convex Optimization.