Coding Theory
These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate st
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201 Jacobus H. van Lint California Institute of Technology, Pasadena, CA/USA
Cod ing Theory Second Printing
Springer-Verlag Berlin · Heidelberg · New York 1973
AMS Subject Classifications (1970): 94A 10
ISBN 3-540-06363-3 Springer-Verlag Berlin - Heidelberg -New York ISBN 0-387-06363-3 Springer-Verlag New York · Heidelberg . Berlin ISBN 3-540-05476-6 1. Auflage Springer-Verlag Berlin· Heidelberg· New York ISBN 0-387-05476-6 1st edition Springer-Verlag New York· Heidelberg· Berlin
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PREFACE These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. and graduate students.
The students who took the course were mathematics seniors Therefore a thorough knowledge of algebra. (a.o. linear
algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed.
After introducing coding theory and linear codes these notes
concern topics mostly from algebraic coding theory. subject, e.g. circuitry, is not included.
The practical side of the
Some topics which one would like to
include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time.
For an extension of the course
into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students.
These are W. W. Peterson's Error-Correcting Codes «(15]),
E. R. Berlekamp's Algebraic Coding Theory «(5]) and several of the AFCRL-reports
by E. F. Assmus, H. F. Mattson and R. Turyn ([2], (3), [4] a.o.).
For several
fruitful discussions I would like to thank R. J. McEliece. The extensive treatment of perfect codes is due to my own interest in this topic and recent developments.
The reader who is familiar with coding theory will
notice that in several places I have given a new treatment or new proofs of known theorems.
Since coding theory is young there remain several parts which need
polishing and several problems are still open.
I sincerely hope that the course
and these notes will contribute to the growing interest of mathematicians in this fascinating subject. For her excellent typing of
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