The algebra of the finite Fourier transform and coding theory-Reference-Cited by-同舟云学术

The algebra of the finite Fourier transform and coding theory

Published:1985 Issue:1 Volume:287 Page:253-273
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Tolimieri R.

Abstract

The role of the finite Fourier transform in the theory of error correcting codes has been explored in a recent text by Richard Blahut. In this work we study how the finite Fourier transform relates to certain polynomial identities involving weight enumerator polynomials of linear codes. These include the generalized MacWilliams identities and theorems originally due to R {\text {R}} . Gleason concerning polynomial algebras containing weight enumerator polynomials. The Heisenberg group model of the finite Fourier transform provides certain algebras of classical theta functions which will be applied to reprove Gleason’s results.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1985-287-01/S0002-9947-1985-0766218-X/S0002-9947-1985-0766218-X.pdf

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