000			03301nam a22006015i 4500
001			978-3-540-30731-0
003			DE-He213
005			20180115171650.0
007			cr nn 008mamaa
008			100301s2006 gw | s |||| 0|eng d
020			_a9783540307310 _9978-3-540-30731-0
024	7		_a10.1007/3-540-30731-1 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aNebe, Gabriele. _eauthor.
245	1	0	_aSelf-Dual Codes and Invariant Theory _h[electronic resource] / _cby Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006.
300			_aXXIV, 406 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAlgorithms and Computation in Mathematics, _x1431-1550 ; _v17
505	0		_aThe 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.
520			_aOne 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 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. It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes. This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists.
650		0	_aMathematics.
650		0	_aCoding theory.
650		0	_aAlgebra.
650		0	_aGroup theory.
650		0	_aNumber theory.
650		0	_aQuantum physics.
650		0	_aControl engineering.
650		0	_aRobotics.
650		0	_aMechatronics.
650	1	4	_aMathematics.
650	2	4	_aAlgebra.
650	2	4	_aCoding and Information Theory.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aControl, Robotics, Mechatronics.
650	2	4	_aNumber Theory.
650	2	4	_aQuantum Physics.
700	1		_aRains, Eric M. _eauthor.
700	1		_aSloane, Neil J.A. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540307297
830		0	_aAlgorithms and Computation in Mathematics, _x1431-1550 ; _v17
856	4	0	_uhttp://dx.doi.org/10.1007/3-540-30731-1
912			_aZDB-2-SMA
999			_c371955 _d371955