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Character sum constructions of constrained error-correcting codes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We estimate parameters of constrained error-correcting codes constructed by means of additive and multiplicative characters. To get the bounds we derive estimates for some incomplete character sums.

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References

  1. Barg, A., Litsyn, S.: DC-constrained codes from Hadamard matrices. IEEE Trans. Inform. Theory37, 3, Part 2, 801–807 (1991)

    Google Scholar 

  2. Barg, A.: Exponential sums and constrained error-correcting codes. Lect. Notes Computer Science, vol. 573, pp. 16–22. Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  3. IEEE Trans. Inform. Theory, Special Issue on Coding for Storage Devices, Part 2 (May 1991)

  4. Levenshtein, V.: Bounds for packings in metric spaces. Problemy Kibernitiki40, 44–110 (in Russian) (1983)

    Google Scholar 

  5. Lidl, R., Niederreiter, H.: Finite Fields. Toronto: Addison-Wesley 1983

    Google Scholar 

  6. MacWilliams, F. J., Sloane, N. J. A.: The Theory of Error-Correcting Codes. Amsterdam: North-Holland 1977

    Google Scholar 

  7. Sarwate, D. V.: An upper bound on the aperiodic autocorrelation function for a maximallength sequence. IEEE Trans. Inform. Theory30(4), 685–687 (1984)

    Google Scholar 

  8. Schmidt, W. M.: Equations over Finite Fields, An Elementary Approach. Lect. Notes Math. vol. 536. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  9. Schouhamer-Immink, K. A.: Coding Techniques for Digital Recorders. Englewood Cliffs: Prentice-Hall 1991

    Google Scholar 

  10. Sidel'nikov, V.: On cross-correlation of sequences. Problemy Kibernetiki24, 15–42 (in Russian) (1971)

    Google Scholar 

  11. Siegel, P.: Recording codes for digital magnetic storage. IEEE Trans. Magn.21, 1344–1349 (1985)

    Google Scholar 

  12. Tietäväinen, A.: Incomplete sums and two applications of Deligne's result. Lect. Notes Math. vol. 1352, pp. 190–205. Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  13. Vinogradov, I. M.: Elements of Number Theory. Dover 1954.

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Authors and Affiliations

  1. Department of Electrical Engineering-Systems, Tel-Aviv University, 69978, Ramat-Aviv, Israel

    Simon Litsyn

  2. Department of Mathematics, University of Turku, SF-20500, Turku, Finland

    Aimo Tietäväinen

Authors
  1. Simon Litsyn
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  2. Aimo Tietäväinen
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Additional information

This work was supported in part by the Academy of Finland. The first-named author would also like to express his gratitude to the Department of Mathematics of the University of Turku for the hospitality during his visit in August, 1992.

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Litsyn, S., Tietäväinen, A. Character sum constructions of constrained error-correcting codes. AAECC 5, 45–51 (1994). https://doi.org/10.1007/BF01196624

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  • DOI: https://doi.org/10.1007/BF01196624

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