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Titlebook: Coding Theory; Jacobus H. Lint Book 1973Latest edition Springer-Verlag Berlin Heidelberg 1973 Finite.algebra.coding.coding theory.error-co

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书目名称Coding Theory
编辑Jacobus H. Lint
视频video
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Coding Theory;  Jacobus H. Lint Book 1973Latest edition Springer-Verlag Berlin Heidelberg 1973 Finite.algebra.coding.coding theory.error-co
描述These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory. The practical side of the subject, e. g. circuitry, is not included. Some topics which one would like to include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time. For an extension of the course into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson‘s Error-Correcting Codes «(15]), E. R. Berlekamp‘s Algebrai
出版日期Book 1973Latest edition
关键词Finite; algebra; coding; coding theory; error-correcting code; finite field; information; mathematics
版次2
doihttps://doi.org/10.1007/978-3-540-36657-7
isbn_softcover978-3-540-06363-6
isbn_ebook978-3-540-36657-7Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 1973
The information of publication is updating

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W. A. Poplawski,J. Piorewicz,M. R. Gourlayr of a prime, q = p.. In this case we can identify these alphabets with the elements of GF(q). We are going to construct ., i.e. codes in which all code words have the same length n which is called the . or ..
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Important cyclic codes,We now introduce a set of multiple-error correcting codes which were discovered by R. C. Bose and D. K. Ray-Chaudhuri and independently by A. Hocquenghem and which are now known as BCH-codes.
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Weight enumeration,There is a remarkable relation between the weight enumerator of a linear code and the weight enumerator of the dual code. The relation was first discovered by F. J. MacWilliams. The proof we give here is based on an idea due to A. M. Gleason.
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Linear codes,r of a prime, q = p.. In this case we can identify these alphabets with the elements of GF(q). We are going to construct ., i.e. codes in which all code words have the same length n which is called the . or ..
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