Introduction to the Theory of Error-Correcting Codes
A complete introduction to the many mathematical tools used to solve practical problems in coding.
Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to solve applied problems.
Introduction to the Theory of Error-Correcting Codes, Third Edition demonstrates this process and prepares students to cope with coding problems. Like its predecessor, which was awarded a three-star rating by the Mathematical Association of America, this updated and expanded edition gives readers a firm grasp of the timeless fundamentals of coding as well as the latest theoretical advances. This new edition features:
* A greater emphasis on nonlinear binary codes
* An exciting new discussion on the relationship between codes and combinatorial games
* Updated and expanded sections on the Vashamov-Gilbert bound, van Lint-Wilson bound, BCH codes, and Reed-Muller codes
* Expanded and updated problem sets.
Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.
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4-tuples algorithm basis BCH code binary code binary cyclic codes binary vectors called code of length codewords coefficients compute consider construct contain coordinate positions Corollary coset leader cyclic shift cyclotomic cosets decoding scheme defined denote dimension divides double-error-correcting doubly-even equations equivalent errors example f-design factor field F finite field g-value GF(p give Gleason polynomials Golay code Hamming code Hence idempotent integers irreducible polynomial Kmod Lemma linear code matrix H minimal polynomial minimum weight modulo monic multiplication nonzero elements number of vectors octad orthogonal parity check matrix permutation polynomial g(x polynomial of degree power moments Problem Proof QR code quadratic residue received vector reciprocal polynomial Reed-Muller codes roots rows of G self-dual code self-orthogonal set of vectors smallest solution Steiner system subspace Suppose syndrome Table ternary Theorem unique vector space vectors of weight weight distribution weight enumerator winning positions Z4 codes zero