Workshop Lectures 1 and 2: Block Codes, Convolutional Codes and Codes on Graphs

Joachim Rosenthal (University of Notre Dame)

The area of coding theory contains many challenging problems where symbolic computations are needed to find solutions. In this tutorial we will give an overview to the field of coding theory.

Coding theory deals with the storage and transmission of information, and the ability to recover the information as completely as possible even if some of the data is lost. A good example is the genetic code stored in a DNA molecule or the ISBN numbers used by book publishers. Modern coding theory started in 1948 with the work of Shannon, who divided it into a stochastic part and an algebraic part. We will concern ourselves with the latter part. In the algebraic sense, a block code can be viewed as an algebraic subset of an affine space over a finite field, hence techniques of algebraic geometry and symbolic computation can be fruitfully applied to the study of codes.

As time allows we will provide an introduction to several important research topics such as convolutional codes, turbo codes and more general codes on graphs. Some of these topics will relate to current research questions and we will treat these topics as time does allow it.