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It is gratifying that this textbook is still sufficiently popular
to warrant a third edition. I have used the opportunity to improve
and enlarge the book. When the second edition was prepared, only
two pages on algebraic geometry codes were added. These have now
been removed and replaced by a relatively long chapter on this
subject. Although it is still only an introduction, the chapter
requires more mathematical background of the reader than the
remainder of this book. One of the very interesting recent
developments concerns binary codes defined by using codes over the
alphabet 7l.4 There is so much interest in this area that a chapter
on the essentials was added. Knowledge of this chapter will allow
the reader to study recent literature on 7l. -codes. 4 Furthermore,
some material has been added that appeared in my Springer Lec ture
Notes 201, but was not included in earlier editions of this book,
e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller
Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's
justification for using error-correcting codes) was added. For the
author, preparing this third edition was a most welcome return to
mathematics after seven years of administration. For valuable
discussions on the new material, I thank C.P.l.M.Baggen, I.
M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson.
A special word of thanks to R. A. Pellikaan for his assistance with
Chapter 10."
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 students.
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. The practical side of the subject, e. g. circuitry,
is not included. 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.
From the reviews: "The 2nd (slightly enlarged) edition of the van Lint's book is a short, concise, mathematically rigorous introduction to the subject. Basic notions and ideas are clearly presented from the mathematician's point of view and illustrated on various special classes of codes...This nice book is a must for every mathematician wishing to introduce himself to the algebraic theory of coding." European Mathematical Society Newsletter, 1993 "Despite the existence of so many other books on coding theory, this present volume will continue to hold its place as one of the standard texts...." The Mathematical Gazette, 1993
Combinatorics, a subject dealing with ways of arranging and distributing objects, involves ideas from geometry, algebra, and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become an essential tool in many scientific fields. In this second edition the authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as graph theory, extremal problems, designs, colorings, and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.
Although graph theory, design theory, and coding theory had their
origins in various areas of applied mathematics, today they are to
be found under the umbrella of discrete mathematics. Here the
authors have considerably reworked and expanded their earlier
successful books on graphs, codes and designs, into an invaluable
textbook. They do not seek to consider each of these three topics
individually, but rather to stress the many and varied connections
between them. The discrete mathematics needed is developed in the
text, making this book accessible to any student with a background
of undergraduate algebra. Many exercises and useful hints are
included througout, and a large number of references are given.
This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.
First published in 1986, the first ICMI study is concerned with the
influence of computers and computer science on mathematics and its
teaching in the last years of school and at tertiary level. In
particular, it explores the way the computer has influenced
mathematics itself and the way in which mathematicians work, likely
influences on the curriculum of high-school and undergraduate
students, and the way in which the computer can be used to improve
mathematics teaching and learning. The book comprises a report of
the meeting held in Strasbourg in March 1985, plus several papers
contributed to that meeting.
This book is concerned with the relations between graphs,
error-correcting codes and designs, in particular how techniques of
graph theory and coding theory can give information about designs.
A major revision and expansion of a previous volume in this series,
this account includes many examples and new results as well as
improved treatments of older material. So that non-specialists will
find the treatment accessible the authors have included short
introductions to the three main topics. This book will be welcomed
by graduate students and research mathematicians and be valuable
for advanced courses in finite combinatorics.
These are notes deriving from lecture courses given by the authors
in 1973 at Westfield College, London. The lectures described the
connection between the theory of t-designs on the one hand, and
graph theory on the other. A feature of this book is the discussion
of then-recent construction of t-designs from codes. Topics from a
wide range of finite combinatorics are covered and the book will
interest all scholars of combinatorial theory.
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