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About Algebraic Coding
Learn the basics of error-control codes and their applications in mathematics and computer science. This packet covers topics such as code parameters, sphere-packing bound, linear codes, ideals, cyclic codes, and BCH codes.
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. citation needed Algebraic coding theory is basically divided into two major types of codes citation needed
This paper surveys the basics of error-correcting codes and their applications in discrete mathematics. It covers linear codes, Hamming codes, cyclic codes, and their properties and examples.
Introduction to Algebraic Coding Theory With Gap Fall 2006 Sarah Spence Adams January 11, 2008 The rst versions of this book were written in Fall 2001 and June 2002 at Cornell University, respectively supported by an NSF VIGRE Grant and a Department of Mathematics Grant.
The mathematical theory of error-correcting codes originated in a paper by Claude Shannon 25 from 1948. A code or a block code C of length n over a nite alphabet F q of size q is a subset C of the set Fn q of all n-letter words with components from F q. We refer to the elements of C as words, codewords, or vectors. A code over F q is
A collection of papers presented at a workshop on algebraic coding theory and information theory held at Rutgers University in December 2003. Topics include fountain codes, expander graphs, low density parity check codes, Reed-Solomon codes, and more.
This chapter introduces some applications of algebra and geometry to coding theory, with examples of linear, cyclic, Reed-Muller and geometric Goppa codes. It is part of a book series on graduate texts in mathematics, published by Springer in 1998.
Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. It makes use of classical and modern algebraic techniques involving finite fields, group theory, and polynomial algebra. It has connections with other areas of discrete mathematics, especially number theory and the theory
This is the revised edition of Berlekamp's famous book, quotAlgebraic Coding Theoryquot, 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
Development Great progress over last sixty years. Some sample results 1950-1960 First families of codes. Algebraic coding theory. Reed-Muller Codes. Reed-Solomon Codes. BCH Codes. 1960-1970 Algorithmic focus intensies. Peterson. Berlekamp-Massey. Gallager - LDPC codes. Forney - Concatenated codes. 1970-1980 Deep theories. Linear Programming bound.