This work addresses the notion of compression ratios greater than what has been known for random sequential strings in binary and larger radix-based systems as applied to those traditionally found in Kolmogorov complexity. A culmination of the author’s decade-long research that began with his discovery of a compressible random sequential string, the book maintains a theoretical-statistical level of introduction suitable for mathematical physicists. It discusses the application of ternary-, quaternary-, and quinary-based systems in statistical communication theory, computing, and physics.