TABLE OF CONTENTS Given a q-ary ( n, M, d)-code, where n is fixed, the size M is a measure of the efficiency of the code, and the distance d is an indication of its error-correcting capability. It would be nice if both M and d could be as large as possible, but, as we shall see shortly in this chapter, this is not quite possible, and a compromise needs to be struck.
For given q, n and d, we shall discuss some well known upper and lower bounds for the largest possible value of M. In the case where M is actually equal to one of the well known bounds, interesting codes such as perfect codes and MDS codes are obtained. We also discuss certain properties and examples of some of these fascinating families.
Let C be a q-ary code with parameters ( n, M, d). Recall from Chapter 2 that the information rate (or transmission rate) of C is defined to be 
( C) = (log q M)/ n. We also introduce here the notion of the relative minimum distance.
For a q-ary code C with parameters ( n, M, d), the relative minimum distance of C is defined to be ?( C) = ( d ? 1)/ n.
