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One of the most remarkable and beautiful theorems in coding
theory is Gleason's 1970 theorem about the weight enumerators of
self-dual codes and their connections with invariant theory, which
has inspired hundreds of papers about generalizations and
applications of this theorem to different types of codes. This
self-contained book develops a new theory which is powerful enough
to include all the earlier generalizations.
The third edition of this definitive and popular book continues to
pursue the question: what is the most efficient way to pack a large
number of equal spheres in n-dimensional Euclidean space? The
authors also examine such related issues as the kissing number
problem, the covering problem, the quantizing problem, and the
classification of lattices and quadratic forms. There is also a
description of the applications of these questions to other areas
of mathematics and science such as number theory, coding theory,
group theory, analogue-to-digital conversion and data compression,
n-dimensional crystallography, dual theory and superstring theory
in physics. New and of special interest is a report on some recent
developments in the field, and an updated and enlarged
supplementary bibliography with over 800 items.
One of the most remarkable and beautiful theorems in coding
theory is Gleason's 1970 theorem about the weight enumerators of
self-dual codes and their connections with invariant theory, which
has inspired hundreds of papers about generalizations and
applications of this theorem to different types of codes. This
self-contained book develops a new theory which is powerful enough
to include all the earlier generalizations.
The third edition of this definitive and popular book continues to
pursue the question: what is the most efficient way to pack a large
number of equal spheres in n-dimensional Euclidean space? The
authors also examine such related issues as the kissing number
problem, the covering problem, the quantizing problem, and the
classification of lattices and quadratic forms. There is also a
description of the applications of these questions to other areas
of mathematics and science such as number theory, coding theory,
group theory, analogue-to-digital conversion and data compression,
n-dimensional crystallography, dual theory and superstring theory
in physics. New and of special interest is a report on some recent
developments in the field, and an updated and enlarged
supplementary bibliography with over 800 items.
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