Self-dual codes and invariant theory
著者
書誌事項
Self-dual codes and invariant theory
（Algorithms and computation in mathematics, v. 17）
Springer, c2006
- : softcover
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注記
Includes bibliographical references (p. [391]-415) and index
内容説明・目次
内容説明
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.
目次
The Type of a Self-Dual Code.- Weight Enumerators and Important Types.- Closed Codes.- The Category Quad.- The Main Theorems.- Real and Complex Clifford Groups.- Classical Self-Dual Codes.- Further Examples of Self-Dual Codes.- Lattices.- Maximal Isotropic Codes and Lattices.- Extremal and Optimal Codes.- Enumeration of Self-Dual Codes.- Quantum Codes.
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