Algebraic soft- and hard-decision decoding of generalized Reed-Solomon and cyclic codes (Q2851163)

The book under review is the PhD dissertation of the author on algebraic coding theory. The key equation for decoding generalized Reed-Solomon codes is reformulated, this allows the author to perform list decoding, both hard and soft decision (in chapter 4 and 5 respectively). In chapter 6, two bounds for bounding the minimum distance of cyclic codes are presented: considering rational functions and embedding the code in a linear cyclic product code, connections with existing bounds are shown. Cyclic codes are decoded defining a key equation, a generalization of the Forney formula is obtained.NEWLINENEWLINEThe book also includes two chapters (chapter 1 and 2) with coding theory preliminaries which facilitates its reading. It also contains open research problems.