Introduction To Algebraic Coding Theory

In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
Contents:

• Vector Space Codes:

  • Linear Codes

• Ring Codes:

  • Rings
  • Ring Codes

• Algebraic Geometry

  • Algebraic Geometry

• Algebraic Geometric Codes:

  • Algebraic Curve Goppa Codes
  • Decoding the Geometric Goppa Codes

• Appendices:

  • Convolution Codes
  • Sphere-Packing Problem and Weight Enumerators
  • Other Important Coding and Decoding Methods
  • Berlekamp's Decoding Algorithm

Readership: Advanced college students, graduate students, working coding theorists, working algebraic geometers.
Key Features:

• Figuratively speaking; the author uses two colors, one for pure Mathematics (namely, Algebra and Algebraic Geometry), the other one for Engineering problems (namely, Coding Theory) to paint an elegant picture