This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory", originally published in 1968, wherein he introduced 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 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.
Both practicing engineers and scholars will find this book to be of great value.
Readership: Researchers in coding theory and cryptography, algebra and number theory, and software engineering.
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This book concerns state-of-the-art coding and decoding methods. Research reviewed in the book include Berlekamp's algorithm for factoring polynomials (the first significant improvement on a classical mathematical problem in almost two centuries), and Berlekamp's algorithm for decoding Bose- Chaudhuri-Hocquenghem and Reed-Solomon codes. For the past 15 years, this coding algorithm has been used universally in algebraic decoders that correct multiple errors in communications or computer memory systems. Chapters include: Basic Binary Codes; Arithmetic Operations Modulo an Irreducible Binary Polynomial; The Number of Irreducible q-ary Polynomials of Given Degree; The Factorization of Polynomials Over Finite Fields; The Enumeration of Information Symbols in BCH Codes; appendices and references.
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Book Description McGraw-Hill Inc.,US, 1968. Hardcover. Book Condition: New. Bookseller Inventory # P110070049033