Industrial Automatic Control Systems and Controllers Annotation << Back Quantitative Estimation of the Size of the Ensemble of Checking Matrices of a Low-Density Code Based on Circulant Matrices M.Yu. Konyshev, P.Yu. Pushkin, S.V. Smirnov, A.V. Bolbenkov The article touches upon the issue of estimating the parameters of a regular low-density code based on circulant matrices. For practical reasons, restrictions are imposed on the length of the code word and a quantitative estimate of the volume of the ensemble of verification matrices of such a code is obtained. The analytical description of the verifi cation matrix of the code and the algorithm of its construction are also given. As a result of the difference between the verifi cation matrix of the lowdensity code from the canonical form of the verifi cation matrix, several schemes for the formation of codes were proposed. The results of the study allowed to determine the volumes of ensembles of verification matrices. Keywords: low-density code, circulant matrix, Galois field, multiplicative order element of the field. DOI: 10.25791/asu.12.2022.1401 Pp. 12-17.