Development of an error correction method using perfect binary arrays

Abstract

The research focuses on an innovative error correction method that uses perfect binary arrays (PBAs), a powerful mathematical tool with unique properties that make it ideal for error correction. The research is aimed at studying the impact of uncorrelated mixed-type errors in the data exchange path, which allows using it in smart technologies with limited computing capabilities. The effectiveness of the approach is confirmed by simulation and comparison with other error correction methods. In order to further study the structural, cross-correlation and distance properties of orthogonal two-dimensional codes and the correcting capabilities of the proposed method, an information technology system for data transmission based on an equivalent class of perfect binary arrays has been developed. The proposed model evaluates the performance of the error correction code based on perfect binary arrays under various conditions, including correlated and uncorrelated interference and data exchange paths. A generator of PBA of equivalent classes has been built. An experimental evaluation of the correcting ability of the proposed two-dimensional codes was carried out by simulating various pre-code situations, including packet and random errors, for the cases of correlated and uncorrelated interference. Using a graphical interface, users will be able to enter the number and type of errors, determine whether they are random or packet errors, manually or automatically, move errors through the data packet, and view intermediate results. Thus, the complex nature of this study can be positioned as a promising approach and a reliable choice in the field of error correction