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001			u370453
003			SIRSI
005			20160812080033.0
007			cr nn 008mamaa
008			110823s2011 xxu| s |||| 0|eng d
020			_a9780817682569 _9978-0-8176-8256-9
040			_cMX-MeUAM
050		4	_aQ350-390
050		4	_aQA10.4
082	0	4	_a519 _223
100	1		_aJoyner, David. _eauthor.
245	1	0	_aSelected Unsolved Problems in Coding Theory _h[recurso electrónico] / _cby David Joyner, Jon-Lark Kim.
250			_a1.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXII, 248p. 17 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_aPreface -- Background -- Codes and Lattices -- Kittens and Blackjack -- RH and Coding Theory -- Hyperelliptic Curves and QR Codes -- Codes from Modular Curves -- Appendix -- Bibliography -- Index.
520			_aUsing an original mode of presentation and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that continue to exist in coding theory. A well-established and still highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite its frequent use in a range of contexts—the first close-up pictures of the surface of Mars, taken by the NASA spacecraft Mariner 9, were transmitted back to Earth using a Reed–Muller code—the subject contains interesting problems that have to date resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGE—a free open-source mathematics software system—to illustrate their ideas, the authors begin by providing background on linear block codes and introducing some of the special families of codes explored in later chapters, such as quadratic residue and algebraic-geometric codes. Also surveyed is the theory that intersects self-dual codes, lattices, and invariant theory, which leads to an intriguing analogy between the Duursma zeta function and the zeta function attached to an algebraic curve over a finite field. The authors then examine a connection between the theory of block designs and the Assmus–Mattson theorem and scrutinize the knotty problem of finding a non-trivial estimate for the number of solutions over a finite field to a hyperelliptic polynomial equation of "small" degree, as well as the best asymptotic bounds for a binary linear block code. Finally, some of the more mysterious aspects relating modular forms and algebraic-geometric codes are discussed. Selected Unsolved Problems in Coding Theory is intended for graduate students and researchers in algebraic coding theory, especially those who are interested in finding current unsolved problems. Familiarity with concepts in algebra, number theory, and modular forms is assumed. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.
650		0	_aMathematics.
650		0	_aCoding theory.
650		0	_aGeometry, algebraic.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aInformation and Communication, Circuits.
650	2	4	_aCoding and Information Theory.
650	2	4	_aSignal, Image and Speech Processing.
650	2	4	_aApplications of Mathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebraic Geometry.
700	1		_aKim, Jon-Lark. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817682552
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-8176-8256-9
596			_a19
942			_cLIBRO_ELEC
999			_c198333 _d198333