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Cyclic codes are used when transmitting information over communication channels, especially in the absence of the possibility of retransmission of data. They are one of the options to reduce the likelihood of communication errors. The article describes the various applications of cyclic codes, and in connection with the multiplicity of these areas, a natural question arises about the number of such codes-for some previously fixed values of the corresponding parameters. In this paper, we consider algorithms that allow us to solve the problem of estimating the number of different noise-resistant codes with given parameters in a general form. Some results have also been obtained for the particular case of cyclic codes, the socalled Bose – Chaudhuri – Hocquenghem codes (BCH-codes). The algorithms considered in the article have a polynomial complexity. All of them were software implemented, and the authors have not only program confirming the theoretical obtained estimating, but also have obtained lists of all possible generating polynomials corresponding to the cyclic codes under consideration with given parameters.

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