Binary Linear Codes, Binary Matrices and graphs: An efficient method for computing the automorphism groups

Harzalla, Driss

ISBN 10: 6202078634 / ISBN 13: 9786202078634

Published by LAP LAMBERT Academic Publishing, 2017

About this Item

84 pages. 8.66x5.91x0.19 inches. In Stock.

Seller Inventory # zk6202078634

Bibliographic Details

• Title: Binary Linear Codes, Binary Matrices and graphs: An efficient method for computing the automorphism groups
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2017
• Language: English
• ISBN 10: 6202078634
• ISBN 13: 9786202078634
• Binding: Paperback
• Condition: Brand New
• Weight: 0.17 kilograms

About this title

Synopsis

After the second World War, Claude Shannon formalized the information theory as a branch of mathematics, posing the problems of reliability and security. Reliability deals with the ability to transmit without error a message despite alterations in communication: it is treated by error correcting codes theory. In 1950, Richard Wesley Hamming worked with Shannon on this subject. He used vector spaces of finite dimension over finite fields to formalize operational framework to the theory and find the first examples of optimal correcting codes. This approach gave rise to the linear codes theory. The automorphism group is useful in: determining the structure of codes, computing weight distributions of codes, determining whether two codes are equivalent, in some decoding algorithms and in group theory. Recall that the classification of finite simple groups has been completed thanks to sporadic groups such as Mathieu groups which was realized as the authomorphism group of Golay codes. This book consists of four Chapter and an Annex. It is intended for PhD students and future engineers. It is also useful for researchers interested in topics of coding theory and cryptography.

About the Author

I hold a PhD in Mathematical Sciences supported at Chouaib Doukkali University. I taught mathematics for twenty three years. I am also an associate member of the Laboratory of Fundamental Mathematics - Chouaib Doukkali University, El Jadida Morocco. The field of my research is applied algebra, the theory of correcting codes and cryptography.