Block codes happen razdelimy and inseparable. Codes in which symbols on their appointment can be divided into the information symbols bearing an about messages and test belong to the razdelimy. Such codes as (n, k), where by n-length of a code, k-number of information symbols. The number of combinations in a code does not exceed 2^k. Codes which symbols cannot be divided on their appointment on information and test belong to the.
Each cyclic code (n, k) is characterized by so generating polynomial. Any (x) n-k degrees can be it. Cyclic codes are characterized by that polynomials of b (x) code combinations share without the rest on (x). Therefore process of coding is reduced to search of a polynomial of b (x) on known polynomials of a (x) and (x), sharing on (x) where a (x) - the polynomial of degree of k-1 corresponding to sequence of symbols.
where In - the vector corresponding to the transferred code. At S=0 decoder makes the decision on absence , and at S≠O - on existence of mistakes. By a concrete type of a syndrome it is possible within ability of a code to point to wrong symbols and them to correct.