ABSTRACT
Coding theory is the study of methods for the efficient and accurate transfer of information from one place to another. This chapter defines a linear error-correcting code, which is often called an algebraic code. It makes considerable use of some of group theoretic ideas, especially those related to subgroups of finite groups and Lagrange’s theorem. Linear codes can be considered over any finite field or even over more general finite rings. The chapter discusses the construction of an infinite class of codes known as Hamming codes and shows that Hamming codes provide the only non-trivial infinite family of perfect codes. One method that is very helpful to construct linear codes involves the use of a generator matrix. The chapter demonstrates the construction of linear codes and provides a brief discussion of perfect codes.
