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Recent Trends in Coding Theory and Its Applications
Edited by: Wen-Ching Winnie Li, Pennsylvania State University, University Park, PA
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
2007; 200 pp; softcover
Volume: 41
ISBN-10: 0-8218-4298-6
ISBN-13: 978-0-8218-4298-0
List Price: US$61
Member Price: US$48.80
Order Code: AMSIP/41
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Coding theory draws on a remarkable selection of mathematical topics, both pure and applied. The various contributions in this volume introduce coding theory and its most recent developments and applications, emphasizing both mathematical and engineering perspectives on the subject. This volume covers four important areas in coding theory: algebraic geometry codes, graph-based codes, space-time codes, and quantum codes. Both students and seasoned researchers will benefit from the extensive and self-contained discussions of the development and recent progress in these areas.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Research mathematicians interested in coding theory.

Table of Contents

Algebraic geometry codes
  • M.-C. Kang -- Introduction to algebraic geometry codes
  • W.-C. W. Li -- Upper and lower bounds for \(A(q)\)
  • W.-C. W. Li -- Elkies' modularity conjecture
  • H. Maharaj -- Explicit towers and codes
  • W.-C. W. Li -- Improved algebraic geometry bounds
  • A. Garcia and H. Stichtenoth -- On the Galois closure of towers
Graph-based codes
  • N. Boston -- Graph-based codes
New aspects of Reed Muller codes
  • A. R. Calderbank -- Reed Muller codes and symplectic geometry
Quantum codes
  • A. Ashikhmin and S. Litsyn -- Foundations of quantum error correction
  • K. Feng -- A new description of quantum error-correcting codes
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