The application of various areas of the theory of coding in the problems of
analysis of the genome includes different areas. For instance, the method for detecting linear
block codes, which takes into account possible insertions and divisions in DNA sequences.
For a lot of such problems, we shall consider the number of codes of the required dimension.
One of the most important such tasks is counting their number. We study this area it in this
paper. We solve the problem of defining the number of cyclic codes over finite field with two
arbitrary fixed parameters. These parameters are n, i.e., the length of the code, and k, i.e.,
the number of information symbols. The algorithm to solve this problem in general is
described in this paper. Also the results at some fixed values are given. We have counted
some constants connected with coding theory, which can be used in some problems of
genome analysis.The authors of the article express their gratitude to Ksenia Krasheninnikova (St. Petersburg
State University, Russia) and Vasily Dolgov (Togliatti State University, Russia) for their detailed
review of the books and articles cited in this paper.
The reported study was partially supported by RFBR according to the research project
No. 16-47-630829
