Estimation of the correcting capability of cyclic codes based on their automation models - Семеренко, Василий Петрович (Eastern-European Journal of Enterprise Technologies, 2015)
We have considered a new method of presenting cyclic codeswith the use of finite automata in binary Galois fields - linear finite-state machine (LFSM). The automatic presentation allows using new positions in the approach to solving the fundamental problem in the theory of error correcting coding, which entails identifyingand correcting the capacity of a given code. Instead of the conventional minimum code distance, which is not a comprehensive description of the code and is difficult to calculate, we suggest direct identifying of the number of detected and corrected errors by the automatic and graphic models of the cyclic code. The paper proves that the structure of LSS zero cycles gives the most accurate assessment that can be applied for different types of errors (both occasional and error packages) as well as for all subclasses of cyclic codes (Hamming, Bose-Chaudhuri-Hocquenghem, Fire, and others). We have presented an algorithm for building an automatic code mode and evaluating its capacity. We have introduced new characteristics of error detection and correction capabilities of cyclic codes. These are ranges of different kinds of errors, with precise indication of the number of random errors and bursts error that are revealed and corrected.