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Interrelation of the Cyclic and Weight Structure of Codes over GF(q) and Proportionality Classes

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Abstract

To determine the weight structure of cyclic codes, we establish an interrelation of the cyclic structure of a code and classes of proportional elements.

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REFERENCES

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

    Google Scholar 

  2. Nili, H., Matrixschaltungen zur Codierung und Decodierung von Gruppen-Code, Arch. Elektr. Ubertrag., 1964, vol. 18, no.9, pp. 555–565.

    Google Scholar 

  3. MacWilliams, F.J. and Sloane, N.J.A., The Theory of Error-Correcting Codes, Amsterdam: North-Holland, 1977. Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Moscow: Svyaz’, 1979.

    Google Scholar 

  4. Peterson, W.W., Error-Correcting Codes, Cambridge: MIT Press, 1961. Translated under the title Kody, ispravlyayushchie oshibki, Moscow: Mir, 1964.

    Google Scholar 

  5. Elspas, B., The Theory of Autonomous Linear Sequential Networks, IRE Trans. Circuit Theory, 1959, vol. 6, pp. 45–60 [Russ. Transl. in Kibern. Sb., 1963, vol. 7, pp. 90–128].

    Google Scholar 

  6. Lidl, R. and Niederreiter, H., Finite Fields, Encyclopedia of Mathematics and Its Applications, vol. 20, Reading: Addison-Wesley, 1983. Translated under the title Konechnye polya, 2 vols., Moscow: Mir, 1988.

    Google Scholar 

  7. Zierler, N., Linear Recurring Sequences, J. Soc. Indust. Appl. Math., 1959, vol. 7, no.1, pp. 31–48 [Russ. Transl. in Kibern. Sb., 1963, vol. 6, pp. 55–79].

    Google Scholar 

  8. 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.

    Google Scholar 

  9. Clark, W.E., Equidistant Cyclic Codes over GF(q), Discrete Math., 1977, vol. 17, no.2, pp. 139–141.

    Google Scholar 

  10. Oganesyan, S., Yagdzyan, V., and Tairyan, V., On a Class of Optimal Cyclic Codes, Proc. 2nd Int. Symp. on Information Theory, Tsahkadsor, Armenia, USSR, 1971, Petrov, P.N. and Csaki, F., Eds., Budapest: Akad. Kiado, 1973, pp. 219–224.

    Google Scholar 

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Authors and Affiliations

  1. Center of Economic Reforms, Baku, Azerbaijan Republic

    I. I. Mullayeva

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  1. I. I. Mullayeva
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Translated from Problemy Peredachi Informatsii, No. 2, 2005, pp. 68–71.

Original Russian Text Copyright © 2005 by Mullayeva.

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Mullayeva, I.I. Interrelation of the Cyclic and Weight Structure of Codes over GF(q) and Proportionality Classes. Probl Inf Transm 41, 130–133 (2005). https://doi.org/10.1007/s11122-005-0018-2

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  • DOI: https://doi.org/10.1007/s11122-005-0018-2

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