Weil Transform and Error Correcting Codes

Abstract

A connection between the Weil transform and error-correcting codes is developed. This contrasts with existing efforts that are based on the Fourier transform and have led to new classes of codes well tailored for burst-error correction. A number of analytical questions must be treated in extending these analogies to the Weil case. In particular, bounds on the mean-square norm of the discrepancy between the FFT (Fast Fourier Transform) and the continuous transform should be established. This was done be consideration of a Riemann sum. The application to information theory then results by applying the Landau-Slepian "approximate dimension theorems" for functions that are only approximately band-limited. Allegations that certain results on "Fourier Transforms for Abelian Groups" which we announced as accomplishments on this grant and a related Darpa grant effort, were actually part of a well-known body of tutorial material are examined and refuted.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 05, 1996
Accession Number
ADA376721

Entities

People

  • Louis Auslander

Organizations

  • City University of New York

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Classification
  • Computations
  • Computer Science
  • Digital Signal Processing
  • Fast Fourier Transforms
  • Frequency
  • Information Theory
  • Materials
  • Mathematics
  • Periodic Functions
  • Permutations
  • Signal Processing
  • Target Recognition
  • Theorems
  • Waveforms

Readers

  • Approximation Theory.
  • Computer Programming and Software Development.
  • Theoretical Analysis.