Abstract
The geometry of finite abelian groups has a long history of significant contributions to many fields in pure and applied mathematics. The arithmetic of this geometry is responsible for some of the deepest and most fruitful formulas in number theory and theta function theory [2]. It forms the basis for many results in algebraic block coding theory [1]. Most often the finite abelian groups come with additional structure, making them into modules and rings relative to which duality can be defined. Duality interleaves the additive group structure with multiplicative structure.
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References
Cameron, P.T. and Van Lint, J.H. (1980), Graphs, Codes and Designs, London Mathematical Society Lecture Note Series 43, Cambridge University Press, Cambridge, Great Britain.
Rauch, H.E. and Farka, H.M. (1974), Theta Functions with Applications to Riemann Surfaces, Williams and Wilkins, Baltimore.
Vulis, M. and Tsai, D. (1990), “Computing Discrete Fourier Transform on a Rectangular Data Array,” IEEE Trans. ASSP ASSP-38(2).
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© 1997 Springer Science+Business Media New York
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Tolimieri, R., An, M., Lu, C. (1997). Lines. In: Burrus, C.S. (eds) Mathematics of Multidimensional Fourier Transform Algorithms. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1948-4_6
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DOI: https://doi.org/10.1007/978-1-4612-1948-4_6
Publisher Name: Springer, New York, NY
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