Finite Fields for Computer Scientists and Engineers

Robert J. McEliece

ISBN 10: 0898381916 / ISBN 13: 9780898381917

Editore: Kluwer Academic Publishers, 1987

Riguardo questo articolo

Ancien livre de bibliothèque avec équipements. Couverture différente. Edition 1987. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Good. Former library book. Different cover. Edition 1987. Ammareal gives back up to 15% of this item's net price to charity organizations. Codice articolo G-128-773

Dati bibliografici

Titolo: Finite Fields for Computer Scientists and ...

Casa editrice: Kluwer Academic Publishers

Data di pubblicazione: 1987

Legatura: Hardcover

Condizione: Bon

Descrizione articolo

Riassunto:

This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ­ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond­ ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char­ acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.

Contenuti:

1 Prologue.- 2 Euclidean Domains and Euclid’s Algorithm.- 3 Unique Factorization in Euclidean Domains.- 4 Building Fields from Euclidean Domains.- 5 Abstract Properties of Finite Fields.- 6 Finite Fields Exist and are Unique.- 7 Factoring Polynomials over Finite Fields.- 8 Trace, Norm, and Bit-Serial Multiplication.- 9 Linear Recurrences over Finite Fields.- 10 The Theory of m-Sequences.- 11 Crosscorrelation Properties of m-Sequences.