ABSTRACT
Binary linear codes are particularly handy for block coding. This chapter describes how block coding works: the incoming data is divided into consecutive blocks of length k. In block coding the length of bitstrings is increased from k to n. The chapter compares the error probabilities with and without coding in a special case, based on the binary symmetric channel. It examines how to describe binary linear codes using either a generator matrix or a check matrix. It is natural to concentrate on the rows of these matrices. However, it will turn out very profitable to change the point of view and read these matrices column wise. The notion of an orthogonal array originated not in information theory but in statistics. It plays a central role in the design of experiments and has many more applications in theoretical computer science and cryptology.
