The Mathematics of Coding Theory Review

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The Mathematics of Coding Theory ReviewIn this book, the emphasis is on the mathematics, it can be considered a book on abstract algebra where the applications are restricted to the creation of codes for the transmission of binary data. Detailed explanations of groups, rings, fields, polynomial fields, primitive roots, and primitive polynomials with theorems and complete proofs are given. Other necessary background material such as probability, combinatorics and linear algebra are included. Overall, the mathematical level is at that of the junior or senior in the math major. There are exercises at the ends of the chapters with some solutions included in an appendix.
While the book has more than enough theory, it is not suitable for a computer science course designed to teach how codes are used in the transmission of data. There are too few concrete examples for it to be used for that purpose. I would not use it for such courses although I would consider using it for a course in abstract algebra, for the applications are those that most modern math majors would understand and appreciate.
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