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

• 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

• N. Boston -- Graph-based codes

• A. R. Calderbank -- Reed Muller codes and symplectic geometry

• A. Ashikhmin and S. Litsyn -- Foundations of quantum error correction
• K. Feng -- A new description of quantum error-correcting codes