Finite Fields for Computer Scientists and Engineers - Robert J. McEliece

Finite Fields for Computer Scientists and Engineers

Buch | Softcover
208 Seiten
2011 | Softcover reprint of the original 1st ed. 1987
Springer-Verlag New York Inc.
978-1-4612-9185-5 (ISBN)
235,39 inkl. MwSt
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 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.
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.

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.

Reihe/Serie The Springer International Series in Engineering and Computer Science ; 23
Zusatzinfo XII, 208 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Sachbuch/Ratgeber Natur / Technik Garten
Mathematik / Informatik Mathematik Algebra
Technik Elektrotechnik / Energietechnik
Schlagworte Algebra
ISBN-10 1-4612-9185-2 / 1461291852
ISBN-13 978-1-4612-9185-5 / 9781461291855
Zustand Neuware
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