Mathematical Theory and Applications of Error-Correcting Codes book presents those concepts of mathematics that continue to reveal essentials in making reliable the data exchange between systems and their parts. For such reason, its applications range over many areas, including physical science, engineering, and medicine. In particular, it treats of hard and soft-decision decoding, of cyclic and quasi-cyclic codes, of Reed-Solomon codes, of low density parity check codes, and quantum error-correcting codes.