Estimation of Independent Errors and Bursts Correction Capability of Linear Codes

The article explores the problem of determining the error-correcting capability of linear codes for simultaneous correction of bursts and independent errors in communication channels affected by memory, similar to those described by a two-state Markov model representing good and bad channel states. Traditional methods for assessing error correction capability rely on standard array, which are computationally expensive. The article introduces an algorithm that, based on the multiplicity of correctable bursts and independent errors, calculates the maximum burst length that can be corrected. This algorithm exhibits polynomial complexity for small numbers of correctable bursts and independent errors. Furthermore, the article provides empirical assessments of the joint error-correcting capability for specific linear codes and estimates the algorithm's computational complexity. These results demonstrate the feasibility of determining error-correcting capability for code lengths significantly exceeding those that standard array can handle. These findings have practical applications for evaluating error-correcting parameters in memory-based communication channels.