chapter  Chapter 11
2 Pages

Summary and outlook

ByJuergen Bierbrauer

This part introduction presents an overview of the key concepts discussed in the subsequent chapters. The part discusses some areas of application which are different from the classical application for information transmission. It focuses on the statistical interpretation of orthogonal arrays as families of random variables with a statistical independence property. The part shows how codes can be interpreted as universal hash classes. It presents a self-contained introduction to geometric algebra over finite fields, the theory of bilinear, sesquilinear and quadratic forms. The part considers a generalization of linear codes. It discusses some recursive and direct constructions as well as applications to computer memory systems and deep-space communication. The part explains that the mechanism of cyclic codes is generalized to additive codes. It describes the general linear-programming bound and presents a very brief sketch of the theory of algebraic-geometric codes. The part explores a list decoding of Reed-Solomon codes.