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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The algebra of the finite Fourier transform and coding theory
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by R. Tolimieri PDF
Trans. Amer. Math. Soc. 287 (1985), 253-273 Request permission

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 ${\text {R}}$. 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.
References
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 287 (1985), 253-273
  • MSC: Primary 94B05; Secondary 22E25, 42A38
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0766218-X
  • MathSciNet review: 766218