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Carte Selected Unsolved Problems in Coding Theory David Joyner

Selected Unsolved Problems in Coding Theory

Autor: David Joyner, Jon-Lark Kim
Limbă: engleză
Legare: Copertă tare
Editura: Birkhauser Boston Inc
Disponibilitate: În depozitul extern
Expediem în 10-13 zile
277.38 lei
Using an original mode of presentation, and emphasizing the computational nature of the subject, thi...

Informații despre carte

Autor
David Joyner, Jon-Lark Kim
Limbă
engleză
Legare
Carte - Copertă tare
Publicat
2011
Pagini
248
EAN
9780817682552
ISBN
0817682554
Enbook ID
01399528
Editura
Birkhauser Boston Inc
Greutate
1060
Dimensiuni
155 x 235 x 16

Descriere completă

Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established, yet 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 still contains interesting unsolved problems that have 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 with the theory of block designs and the Assmus Mattson theorem. Further chapters 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. Some of the more mysterious aspects relating modular forms and algebraic-geometric codes are also 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 some 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.

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