Introduction To The Theory Of Error-correcting Codes
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Vera Pless ISBN: 978-0-471-19047-9 224 pages July 1998 Description A complete introduction to the many introduction to the theory of error-correcting codes pdf mathematical tools used to solve practical problems in coding. Mathematicians
Introduction To The Theory Of Error-correcting Codes Vera Pless Pdf
have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers the theory of error correcting codes macwilliams pdf 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 fundamentals of error-correcting codes 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
Hamming Code
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. See More See Less Table of Contents Introductory Concepts. Useful Background. A Double-Error-Correcting BCH Code and a Finite Field of 16 Elements. Finite Fields. Cyclic Codes. Group of a Code and Quadratic Residue (QR) Codes. Bose
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to the Theory of Error-Correcting Codes, Third EditionArticle in Mathematics of Computation 56(193) · June 1991 with 10 ReadsDOI: 10.2307/2008564 1st Vera PlessAbstractHalf TitleSeries InfoTitleCopyrightDedicationContentsPrefaceDo you want to read the https://www.researchgate.net/publication/265546859_Introduction_to_the_Theory_of_Error-Correcting_Codes_Third_Edition rest of this article?Request full-text CitationsCitations168ReferencesReferences0Error-correcting codes from $k$-resolving sets"Traditionally, the most familiar error-correcting codes are linear codes (i.e. subspaces of vector spaces over finite fields) [19], where the alphabet size is small (such as binary codes, which have an alphabet of size 2). Other classes of codes include permutation codes [7], where each codeword is a of error permutation of n symbols, so the length and alphabet size are both equal to n; codes with larger alphabet sizes have been the subject of more recent attention, in part because of applications such as powerline communications [9] and flash memory devices [23]. "[Show abstract] [Hide abstract] ABSTRACT: We demonstrate a construction of error-correcting codes from graphs by the theory of means of $k$-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the $k$-metric dimension of grid graphs (i.e. Cartesian products of paths). Full-text · Article · May 2016 Robert F. BaileyIsmael G. YeroRead full-textOn the number of alternating paths in bipartite complete graphs"Let α r (m, t) be the maximum size of a code C ⊆ [r] m such that any two elements of C have Hamming distance at least t. We refer the reader to [9] for more details concerning coding theory. Let K m,n be a complete bipartite graph on vertex set [m] ∪ [n]. "[Show abstract] [Hide abstract] ABSTRACT: Let $C \subseteq [r]^m$ be a code such that any two words of $C$ have Hamming distance at least $t$. It is not difficult to see that determining a code $C$ with the maximum number of words is equivalent to finding the largest $n$ such that there is an $r$-edge-coloring of $K_{m, n}$ with the property that any pair of v
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