Algebraic Coding Theory

Algebraic Coding Theory

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This is the revised edition of Berlekamp's famous book, qAlgebraic Coding Theoryq, 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 Bosea€“Chaudhuria€“Hocquenghem codes that subsequently became known as the Berlekampa€“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. Contents:Basic Binary CodesArithmetic Operations Modulo An Irreducible Binary PolynomialThe Number of Irreducible q-ary Polynomials of Given DegreeThe Structure of Finite FieldsCyclic Binary CodesThe Factorization of Polynomials Over Finite FieldsBinary BCH Codes for Correcting Multiple ErrorsNonbinary CodingNegacyclic Codes for the Lee MetricGorenstein-Zierler Generalized Nonbinary BCH Codes for the Hamming MetricLinearized Polynomials and Affine PolynomialsThe Enumeration of Information Symbols in BCH CodesThe Information Rate of the Optimum CodesCodes Derived by Modifying or Combining Other CodesOther Important Coding and Decoding MethodsWeight EnumeratorsAppendices and References Readership: Researchers in coding theory and cryptography, algebra and number theory, and software engineering. Key Features:A classic monograph and reference book on Coding Theory and Cryptography written by a revered scholar long known for his work in coding theoryContains several theorems created by the author that have been respected for 40 yearsKeywords:Coding Theory;Binary Codes;Irreducible Q-ary Polynomial;Error-Correcting Codes;BCH Codes;Berlekamp's Algorithm;Finite Fields... 318a€“324 error, asymptotic, 324-329 for concatenated codes, 348 with feedback, 328-329 Gilbo, 321-324, 328-329, ... vii, 11, 208 (See also under BCH; Bose) Chebyshev polynomials over GF(2), 118 Check digits, 1a€“8 (See also Informationanbsp;...

Title:Algebraic Coding Theory
Author: Elwyn R Berlekamp
Publisher:World Scientific - 2015-03-26

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