Self-Dual Codes and Invariant Theory

• Κύριοι συγγραφείς: Nebe, Gabriele (Συγγραφέας), Rains, Eric M. (Συγγραφέας), Sloane, Neil J.A (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Algorithms and Computation in Mathematics, 17
• Θέματα: Mathematics.; Coding theory.; Algebra.; Group theory.; Number theory.; Quantum physics.; Control engineering.; Robotics.; Mechatronics.; Coding and Information Theory.; Group Theory and Generalizations.; Control, Robotics, Mechatronics.; Number Theory.; Quantum Physics.

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. In the past 35 years there have been hundreds of papers written about generalizations and applications of thi...

Πίνακας περιεχομένων:

• 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.