Even-Length Modified Linear Block Code for Space Links

This work introduces a new technique for constructing enhanced-distance linear block codes tailored for binary vector systems with even dimensions. The approach is based on the theory of completely controllable discrete-time systems, where the solution space of such systems is systematically adapted to generate the code structure. As a demonstration, a controllable system of order 20 is used to design a (40,20) block-structured linear code, corresponding to an information rate of 0.5. To strengthen the error-correcting capability, a specialized mapping method is applied, which increases the minimum separation among valid code words by permuting the binary vectors. By widening this distance, the code exhibits improved tolerance to transmission errors. Simulation studies show that the suggested design achieves a lower Bit-Error Rate (BER) and a smaller probability of undetected errors compared with other block codes having the same parameters. These attributes make the scheme highly suitable for applications requiring exceptional reliability, such as deep-space communication, where both accuracy and robustness are critical. The results highlight how integrating concepts from control theory with modern coding strategies can produce efficient error-correcting codes for demanding communication systems, and they point toward future research opportunities in control-based code design for advanced data transmission.