This paper presents a comprehensive analysis and implementation of various error correction coding methods, focusing on Reed-Solomon (RS) codes and Liberation codes in RAID6 systems. RS codes are emphasized for their robust error correction capabilities, making them ideal for high-reliability environments such as enterprise data centers and mission-critical systems, where the ability to correct multiple errors or data losses is crucial. In contrast, Liberation codes are noted for their superior encoding efficiency and lower computational complexity, making them well-suited for high-performance systems with stringent speed requirements. Through experimental comparisons, this study also evaluates Cauchy Reed-Solomon (CRS) codes, EVENODD codes, and Blaum-Roth (BR) codes, identifying the strengths and weaknesses of each method in various scenarios. The findings underscore the importance of selecting the appropriate coding technique based on system-specific requirements, as different use cases benefit from different error correction schemes in terms of performance and data reliability. Additionally, this research highlights the potential of these coding methods in broader distributed storage applications and discusses the trade-offs between them. Future research directions are suggested, particularly in optimizing existing codes and expanding their application in more complex and distributed storage environments.