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Construction of generator polynomials for residue codes of degrees 5–8

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Moscow University Mathematics Bulletin Aims and scope

Abstract

A generalization of quadratic residue codes to the case of higher degree is considered. Properties of h-power residue codes are studied. In some cases, it is possible to indicate the form and method of construction of a generator polynomial. Using the results obtained here, generator polynomials for residue codes of degrees 5–8 are constructed.

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References

  1. F. J, MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North Holland Publ. Comp., Amsterdam, New York, Oxford, 1977; Svyaz’, Moscow, 1979).

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  2. D. N. Semenovykh, “Number-Theoretical Problems in Coding Theory,” Candidate’s Dissertation in Mathematics (Moscow, 2006).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. L. Artamonov

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  1. A. L. Artamonov
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Original Russian Text © A.L. Artamonov, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 6, pp. 9–15.

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Artamonov, A.L. Construction of generator polynomials for residue codes of degrees 5–8. Moscow Univ. Math. Bull. 68, 7–13 (2013). https://doi.org/10.3103/S0027132213010026

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  • DOI: https://doi.org/10.3103/S0027132213010026

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