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Field name	Details
Dewey Class	519
Title	Selected Unsolved Problems in Coding Theory ([EBook]) / by David Joyner, Jon-Lark Kim.
Author	Joyner, David. , 1959-
Added Personal Name	Kim, Jon-Lark
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2011.
Physical Details	XII, 248 pages : 17 illus. : online resource.
Series	Applied and numerical harmonic analysis
ISBN	9780817682569
Summary Note	Using an original mode of presentation and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems thatÂ 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 ReedâMuller code the subject contains interesting problems that have to date resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGEâa 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 connectionÂ between the theory of block designs and the AssmusâMattson 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.:
Contents note	Preface -- Background -- Codes and Lattices -- Kittens and Blackjack -- RH and Coding Theory -- Hyperelliptic Curves and QR Codes -- Codes from Modular Curves -- Appendix -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to susbcription institutions through IP address (only for SISSA users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8256-9
Links to Related Works	Subject References: Algebraic Geometry . Applications of Mathematics . Coding and Information Theory . Coding theory . Geometry, Algebraic . Information and communication, circuits . Number Theory . Signal, Image and Speech Processing . Authors: author . Joyner, David. 1959- . Kim, Jon-Lark . Corporate Authors: SpringerLink (Online service) . Series: Applied and numerical harmonic analysis . Classification: 519 .

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Selected Unsolved Problems in Coding Theory

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