Algebraic coding theory. (English) Zbl 0988.94521

Berlekamp, Elwyn R.

New York, NY: McGraw-Hill Book. xiv, 466 p. (1968).

Publisher’s description: Herein the author introduces several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem (BCH) codes that subsequently became known as the Berlekamp-Massey algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes. Selected chapters of the book became a standard graduate textbook.
See also the review of the Russian translation (Mir, Moskva) (1971; Zbl 0256.94006). A more detailed review written by C. T. Chien can be found in [IEEE Trans. Inf. Theory 15, No. 4, 509–510 (1969), doi:10.1109/TIT.1969.1054318].

MSC:

94Bxx	Theory of error-correcting codes and error-detecting codes
94-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory

Citations:

Zbl 0256.94006