Abstract
We consider partitions of finite abelian groups. We introduce the concept of Fourier-invariant pairs and demonstrate that this concept is equivalent to the concept of an association scheme in an abelian group. It follows that Fourier-invariant pairs of partitions might be viewed as a very natural approach to abelian association schemes.
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Original Russian Text © V.A. Zinoviev, T. Ericson, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 3, pp. 33–44.
Supported in part by the Russian Foundation for Basic Research, project no. 09-01-00536.
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Zinoviev, V.A., Ericson, T. Fourier-invariant pairs of partitions of finite abelian groups and association schemes. Probl Inf Transm 45, 221–231 (2009). https://doi.org/10.1134/S003294600903003X
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DOI: https://doi.org/10.1134/S003294600903003X