Algebraic Coding Theory
In this chapter we will discuss some applications of techniques from computational algebra and algebraic geometry to problems in coding theory. After a preliminary section on the arithmetic of finite fields, we will introduce some basic terminology for describing error-correcting codes. We will study two important classes of examples—linear codes and cyclic codes—where the set of codewords possesses additional algebraic structure, and we will use this structure to develop good encoding and decoding algorithms. Finally, we will introduce the Reed-Muller and geometric Goppa codes, where algebraic geometry is used in the construction of the code itself.
KeywordsFinite Field Linear Code Block Length Cyclic Code Hilbert Function
Unable to display preview. Download preview PDF.