By Marvin Marcus, Henryk Minc

ISBN-10: 0395048354

ISBN-13: 9780395048351

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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.

### Algebra and Trigonometry by Marvin Marcus, Henryk Minc

by Mark

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