One of the problems in the development of mathematical theory of the genetic code (summary is presented in [
1], the detailed—to [
2]) is the problem of the calculation of the genetic code. Similar problem in the world is unknown and could be delivered only in the 21st century. One approach to solving this problem is devoted to this work. For the first time a detailed description of the method of calculation of the genetic code was provided, the idea of which was first published earlier [
3]), and the choice of one of the most important sets for the calculation was based on an article [
4]. Such a set of amino acid corresponds to a complete set of representation of the plurality of overlapping triple gene belonging to the same DNA strand. A separate issue was the initial point, triggering an iterative search process all codes submitted by the initial data. Mathematical analysis has shown that the said set contains some ambiguities, which have been founded because of our proposed compressed representation of the set. As a result, the developed method of calculation was reduced to two main stages of research, where at the first stage only single-valued domains were used in the calculations. The proposed approach made it possible to significantly reduce the amount of computation at each step in this complex discrete structure.