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Fourier-invariant pairs of partitions of finite abelian groups and association schemes

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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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References

  1. MacWilliams, F.J., A Theorem on the Distribution of Weights in a Systematic Code, Bell Syst. Tech. J., 1963, vol. 42, no. 1, pp. 79–94.

    MathSciNet  Google Scholar 

  2. Delsarte, P., An Algebraic Approach to the Association Schemes of Coding Theory, Philips Res. Rep. Suppl., 1973, no. 10. Translated under the title Algebraicheskii podkhod k skhemam otnoshenii teorii kodirovaniya, Moscow: Mir, 1976.

  3. Zinoviev, V.A. and Ericson, T., On Fourier-Invariant Partitions of Finite Abelian Groups and the MacWilliams Identity for GroupCo des, Probl. Peredachi Inf., 1996, vol. 32, no. 1, pp. 137–143 [Probl. Inf. Trans. (Engl. Transl.), 1996, vol. 32, no. 1, pp. 117–122].

    Google Scholar 

  4. Ericson, T., Simonis, J., Tarnanen, H., and Zinoviev, V., F-Partitions of Cyclic Groups, Appl. Algebra Engrg. Comm. Comput., 1997, vol. 8, no. 5, pp. 387–393.

    Article  MATH  MathSciNet  Google Scholar 

  5. Herstein, I.N., Topics in Algebra, New York: Blaisdell, 1964.

    MATH  Google Scholar 

  6. Bannai, E. and Ito, T., Algebraic Combinatorics I: Association Schemes. Menlo Park: Benjamin/Cummings, 1984.

    MATH  Google Scholar 

  7. Bose, R.C. and Shimamoto, T., Classification and Analysis of Partially Balanced Incomplete Block Designs with Two Associate Classes, J. Amer. Statist. Assoc., 1952, vol. 47, pp. 151–184.

    Article  MATH  MathSciNet  Google Scholar 

  8. Camion, P., Codes and Association Schemes, Handbook of CodingThe ory, Pless, V.S. and Huffman, W.C., Eds., Amsterdam: Elsevier, 1998, pp. 1441–1568.

    Google Scholar 

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Correspondence to V. A. Zinoviev.

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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

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