Weight distribution of binary cyclic codes having the all-one vector: Group of cyclic shifts on codewords of a cyclic code

Kamanga, Suzgo Mnyamula

ISBN 10: 3659542849 ISBN 13: 9783659542848

Editorial: LAP LAMBERT Academic Publishing, 2019

Idioma: Ingl�s

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56 pages. 8.66x5.91x0.13 inches. In Stock.

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T�tulo

Weight distribution of binary cyclic codes having the all-one vector: Group of cyclic shifts on codewords of a cyclic code

Editor

LAP LAMBERT Academic Publishing

Fecha de publicaci�n

2019

Idioma

Ingl�s

ISBN 10

3659542849

ISBN 13

9783659542848

Encuadernaci�n

Paperback

Estado

Brand New

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Sinopsis

In coding theory there are a number of codes which are studied. In this book we specifically consider a class of codes known as cyclic codes. This class of codes has a very nice algebraic structure. We are mainly going to examine weight distribution of a binary cyclic codes which contain the all-one vector. Weight distribution is said to provide information of both practical and theoretical significance. In this book we have used the group of cyclic shifts to examine the weight distribution of binary cyclic code. The group of cyclic shifts acts and fixes elements in the set of all codewords of a cyclic code. As a result of this, stabilizers and lengths of the orbits are established. The lengths of the orbits and their frequencies are used to obtain the weight distribution. Furthermore, we have shown that if the length of a cyclic code is an odd prime and two codewords the all-one and the all-zero are removed from a cyclic code then the number of codewords remaining is divisible by the length. The analysis and results in this book are useful to all mathematicians.

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