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A method for computation of the discrete Fourier transform over a finite field

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Abstract

The discrete Fourier transform over a finite field finds applications in algebraic coding theory. The proposed computation method for the discrete Fourier transform is based on factorizing the transform matrix into a product of a binary block circulant matrix and a diagonal block circulant matrix.

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References

  1. Wang, Y. and Zhu, X., A Fast Algorithm for the Fourier Transform over Finite Fields and Its VLSI Implementation, IEEE J. Select. Areas Commun., 1988, vol. 6, no. 3, pp. 572–577.

    Article  Google Scholar 

  2. Afanasyev, V., On Complexity of FFT over Finite Field, in Proc. 6th Joint Swedish-Russian Int. Workshop on Information Theory, Mölle, Sweden, 1993, pp. 315–319.

  3. Trifonov, P.V. and Fedorenko, S.V., A Method for Fast Computation of the Fourier Transform over a Finite Field, Probl. Peredachi Inf., 2003, vol. 39, no. 3, pp. 3–10 [Probl. Inf. Trans. (Engl. Transl.), 2003, vol. 39, no. 3, pp. 231–238].

    MATH  MathSciNet  Google Scholar 

  4. Rader, C.M., Discrete Fourier Transforms when the Number of Data Samples Is Prime, Proc. IEEE, 1968, vol. 56, no. 6, pp. 1107–1108.

    Article  Google Scholar 

  5. Blahut, R.E., Theory and Practice of Error Control Codes, Reading: Addison-Wesley, 1983. Translated under the title Teoriya i praktika kodov, kontroliruyushchikh oshibki, Moscow: Mir, 1986.

    MATH  Google Scholar 

  6. Bassalygo, L.A., private communication, 2003.

  7. Gantmakher, F.R., Teoriya matrits, Moscow: Nauka, 1988, 4th ed. Translated under the title The Theory of Matrices, 2 vols., Providence: AMS Chelsea, 1998.

    MATH  Google Scholar 

  8. Blahut, R.E., Fast Algorithms for Digital Signal Processing, Reading: Addison-Wesley, 1985. Translated under the title Bystrye algoritmy tsifrovoi obrabotki signalov, Moscow: Mir, 1989.

    MATH  Google Scholar 

  9. van der Waerden, B.L., Algebra, Berlin: Springer, 1971, 8 ed. Translated under the title Algebra, Moscow: Nauka, 1976.

    MATH  Google Scholar 

  10. Costa, E., Fedorenko, S.V., and Trifonov, P.V., On Computing the Syndrome Polynomial in Reed-Solomon Decoder, Eur. Trans. Telecommun., 2004, vol. 15, no. 4, pp. 337–342.

    Article  Google Scholar 

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Original Russian Text © S. V. Fedorenko, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, pp. 81–93.

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Fedorenko, S.V. A method for computation of the discrete Fourier transform over a finite field. Probl Inf Transm 42, 139–151 (2006). https://doi.org/10.1134/S0032946006020074

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  • DOI: https://doi.org/10.1134/S0032946006020074

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