Abstract
The finite Fourier-transform is considered as a linear transformation on a certain space of theta functions and thereby is seen to induce an invertible morphism of Abelian varieties. This is explained in the context of the representation theory of the finite symplectic group. Finally the MacWilliams identities in coding theory are discussed in the light of the theory of theta functions.
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© 1986 Springer-Verlag Berlin Heidelberg
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Opolka, H. (1986). The finite Fourier-transform and theta functions. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_719
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DOI: https://doi.org/10.1007/3-540-16776-5_719
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