A With-Carry Walsh Transform

(Extended Abstract)
  • Andrew Klapper
  • Mark Goresky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


We introduce an arithmetic Walsh transform. It is a with-carry analog, based on modular arithmetic, of the usual Walsh transform of Boolean functions. This is part of our continuing effort to define and investigate with-carry analogs of discrete algebraic structures used in various aspects of communications. We develop tools for analyzing arithmetic Walsh transforms. We prove that the mapping from a Boolean function to its arithmetic Walsh transform is injective. We compute the average arithmetic Walsh transforms and the arithmetic Walsh transforms of affine functions.


Walsh transform 2-adic numbers Boolean functions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andrew Klapper
    • 1
  • Mark Goresky
    • 2
  1. 1.Department of Computer ScienceUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsInstitute for Advanced StudyPrincetonUSA

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