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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The algebra of the finite Fourier transform and coding theory


Author: R. Tolimieri
Journal: Trans. Amer. Math. Soc. 287 (1985), 253-273
MSC: Primary 94B05; Secondary 22E25, 42A38
MathSciNet review: 766218
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766218-X
PII: S 0002-9947(1985)0766218-X
Article copyright: © Copyright 1985 American Mathematical Society