METHODS FOR FORMING BLOCK CYCLIC CODES

Abstract

Issues on constructing systematic and non-systematic cyclic codes used in many modern data processing systems, such as the transmission of audio and video information, reading and writing on CD, DVD, computer networks, etc are considered. Block cyclic codes are redundant codes, at whose construction, correcting symbols are added to the information symbols, allowing to detect and correct the errors. The correction ability of such codes depends on the system of the rules used for their construction, as well as the code length, the number of redundant symbols, etc. In cyclic codes, every new combination is generated by shifting the previous permissible one right or left by one digit. In this case, the resulting combination is also permissible. At studying the cyclic codes, polynomials are convenient means of algebraic descriptions, as it is possible to apply the known transformations of polynomials. The basis for the formation of these codes are the generator polynomials, which are selected from the corresponding irreducible polynomials. An irreducible polynomial is the one that does not expand on polynomials over a lower degree. This means that a polynomial is divisible only by one and by itself. The technical realization of such codes is quite simple, because it is based on shift registers. However, despite the ease of implementation, the mathematical instrument to describe these codes is rather complicated. It is known that the decoding procedure is more complicated than the encoding process. Simple enough for cyclic codes is decoding, which is based on the calculation of the syndrome. Using the rules of operations on polynomials, the methodology and features of constructing cyclic codes on different examples are shown.