J. H. van Lint's Introduction to Coding Theory (3rd Edition) (Graduate Texts PDF

By J. H. van Lint

ISBN-10: 3540641335

ISBN-13: 9783540641339

"The second (slightly enlarged) variation of the van Lint's ebook is a brief, concise, mathematically rigorous advent to the topic. easy notions and ideas are in actual fact provided from the mathematician's viewpoint and illustrated on a number of particular periods of codes...This great e-book is a needs to for each mathematician wishing to introduce himself to the algebraic idea of coding. " eu Mathematical Society publication, 1993 "Despite the lifestyles of such a lot of different books on coding idea, this current quantity will proceed to carry its position as one of many usual texts..." The Mathematical Gazette, 1993

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Extra resources for Introduction to Coding Theory (3rd Edition) (Graduate Texts in Mathematics, Volume 86)

Sample text

2. Sometimes the weight enumerator of a code C is given in homogeneous form as Hamc;(x,y):= Lx"-W(C)yW(C). (x, y) = jCjHamc;(x + y, x - y). 3. 6. The Lee Metric In many communication schemes used in practice, one can model the alphabet as a set of points regularly spaced on a circle. Take as example an alphabet of this kind with seven symbols. 6. The Lee Metric 43 make all errors equally likely. It is much more likely that a transmitted symbol is received as a symbol close to it. In our terminology, this means that if a 4 is sent and an error occurs, it is more likely that a 3 or a 5 is received than a 2 or a 6, etc.

8». We construct a code C with codewords 0, 1, the rows of t(S + I + J) and t( -S + I + J). 8 it follows that C is an (n, 2(n + 1), d) code, where d = t(n - 1) if n == 1 (mod 4) and d = t(n - 3) if n == 3 (mod 4). ] 4. 2. The Binary Golay Code The most famous of all (binary) codes is the so-called binary Golay code f§23' There are very many constructions of this code, some of them quite elegant and with short proofs of the properties of this code. We shall prove that f§24' the extended binary Golay code, is unique and treat a few constructions.

Sometimes the weight enumerator of a code C is given in homogeneous form as Hamc;(x,y):= Lx"-W(C)yW(C). (x, y) = jCjHamc;(x + y, x - y). 3. 6. The Lee Metric In many communication schemes used in practice, one can model the alphabet as a set of points regularly spaced on a circle. Take as example an alphabet of this kind with seven symbols. 6. The Lee Metric 43 make all errors equally likely. It is much more likely that a transmitted symbol is received as a symbol close to it. In our terminology, this means that if a 4 is sent and an error occurs, it is more likely that a 3 or a 5 is received than a 2 or a 6, etc.

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Introduction to Coding Theory (3rd Edition) (Graduate Texts in Mathematics, Volume 86) by J. H. van Lint


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