Binary Correcting Codes with Maximum Coding Rate

This study focuses on the design of binary linear error-correcting codes that achieve the highest possible coding rate while satisfying constraints on codeword length and minimum code distance. Through detailed computational analysis, the research identifies optimal generating codeword combinations, enabling the construction of non-separable linear binary block codes tailored for efficient data transmission in infocommunication systems. The findings include calculated results and corresponding graphs that illustrate code constructions for various codeword lengths and minimum distances. A recursive algorithm facilitates the development of these codes, and a method is proposed to transform them into separable linear codes for practical applications. The research also reveals that the coding rate varies depending on the bit position from which the codeword search begins, impacting code performance. Comparisons with standard codes, such as the BCH code, show differences in weight spectra, which influence error correction capabilities under interference. These insights guide the optimization of reliable, high-efficiency codes for bandwidth-constrained environments.