Bounds on Codes

In this chapter we shall be interested in codes that have as many codewords as possible, given their length and minimum distance. We shall not be interested in questions like usefulness in practice, encoding or decoding of such codes. We again consider as alphabet a set Q of q symbols and we define θ := (q – 1)/q. Notation is as in Section 3.1. We assume q has been chosen and then define an (n, *, d) code as a code with length n and minimum distance d. We are interested in the maximal number of codewords (i.e. the largest M which can be put in place of the *). An (n, M, d) code which is not contained in any (n, M + 1, d) code is called maximal.