Gabriele Nebe's Books

Self-Dual Codes and Invariant Theory

By: Gabriele Nebe,Eric M. Rains,Neil J. A. Sloane

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Self-Dual Codes and Invariant Theory

By: Gabriele Nebe,Eric M. Rains,Neil J. A. Sloane

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.

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Page Count

474

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354030729X

ISBN 13

9783540307297

Finite Rational Matrix Groups

By: Gabriele Nebe,Wilhelm Plesken

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Finite Rational Matrix Groups

By: Gabriele Nebe,Wilhelm Plesken

The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and p +1 and p-1 for all prime numbers p. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.

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