文档介绍：The Carus Mathematical Monographs
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NUMBER TWENTY-ONE
FROM ERROR-CORRECTING
CODES THROUGH SPHERE
PACKINGS TO SIMPLE GROUPS
THOMAS M. THOMPSON
Walla Walla College
Published and Distributed by
THE MATHEMATICAL ASSOCIATION OF AMERICA
PREFACE
Back in 1947 Richard W. Hamming had access to -
puter only on weekends. Some three decades later he recalled
his frustration over its perverse behavior:
Two weekends in a row I came in and found that all my stuff had
been dumped and nothing was done. . . .And so I said, 'Damn it,
if the machine can detect an error, why can't it locate the position
of the error and correct it?' [56, Tape 21
That question initiated the development of error-correct-
ing codes. The puter, a mechanical relay
model at Bell Telephone Laboratories, always came to an
angry stop and switched to the next program whenever it de-
tected an error. This behavior impelled Hamming, a pure
mathematician with an applied bent, to devise the first error-
correcting code.
We shall follow the devious trail that wends its way
through a quarter-century of mathematics, starting with
0 1983 by
The Mathematical Association of America Ilncorporated) Hamming's work, which led almost immediately to that of
Library of Congress Catalog Card Number 82-062784 M. J. E. Golay. The latter sparked, some twelve years later,
giant steps in the packing of congruent spheres by John
Complete Set ISBN 0-88385-000-1 Leech, which, in turn, branched off through the work of J. H.
Voi. 21 ISBN 0-88385-023-0 Conway, into the field of simple groups. By tracing some of
the twists, turns, switchbacks and dead ends of this path, we
Printed in the United States of America hope to provide a small window on the history of mathemat-
ics of the twentieth century. How historians ultimately will
Current printing (last digit):
treat this golden age of mathematical creativity we cannot
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