Error-Correcting Linear Codes Classification by Isometry and Applications /

• Main Authors: Betten, Anton (Author), Braun, Michael (Author), Fripertinger, Harald (Author), Kerber, Adalbert (Author), Kohnert, Axel (Author), Wassermann, Alfred (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Algorithms and Computation in Mathematics, 18
• Subjects: Mathematics.; Coding theory.; Algebra.; Algorithms.; Combinatorics.; Coding and Information Theory.; Signal, Image and Speech Processing.

This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group a...

Table of Contents:

• Linear Codes
• Bounds and Modifications
• Finite Fields
• Cyclic Codes
• Mathematics and Audio Compact Discs
• Enumeration of Isometry Classes
• Solving Systems of Diophantine Linear Equations
• Linear Codes with a Prescribed Minimum Distance
• The General Case.