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008			150903s2011 xxu| o |||| 0|eng d
020			_a9780817682569 _99780817682569
024	7		_a10.1007/9780817682569 _2doi
035			_avtls000333717
039		9	_a201509030218 _bVLOAD _c201404130520 _dVLOAD _c201404092309 _dVLOAD _y201402041118 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQ350-390
100	1		_aJoyner, David. _eautor _9307417
245	1	0	_aSelected Unsolved Problems in Coding Theory / _cby David Joyner, Jon-Lark Kim.
250			_a1.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_axii, 248 páginas 17 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aApplied and Numerical Harmonic Analysis
500			_aSpringer eBooks
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.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aKim, Jon-Lark. _eautor _9307418
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9780817682552
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-8176-8256-9 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c281604 _d281604