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Mathematics of Computation

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Existence theorems for transforms over finite rings with applications to $ 2$-D convolution


Author: David P. Maher
Journal: Math. Comp. 35 (1980), 757-765
MSC: Primary 10-04; Secondary 94B35
DOI: https://doi.org/10.1090/S0025-5718-1980-0572853-3
MathSciNet review: 572853
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Abstract: An existence theorem for Fourier-like transforms over arbitrary finite commutative rings is proven in a simple fashion. Corollaries for the case of residue class rings over the integers and extensions of those rings follow directly. The theory is applied to construct very fast algorithms for the computation of two-dimensional convolutions over the integers $ \bmod\, M$.


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DOI: https://doi.org/10.1090/S0025-5718-1980-0572853-3
Article copyright: © Copyright 1980 American Mathematical Society