Let K be a finite field and let V be the vector space of n-tuples over K. The Hamming-distance between elements x and y of V, denoted d(x, y), is defined by d(x, y) := #{ 1 <= i <= n | x_i != y_i }. The minimum distance d for a subset C of V is then d = min{ d(x, y) | x in C, y in C }. The subset C of V is called an (n, M, d) code if the minimum distance for the subset C is d and |C| = M. The code C is called a [n, k, d] linear code if C is a k-dimensional subspace of V. V is then also called the ambient space of C.

Magma currently supports only linear codes. In the following, the term "code" will refer to a linear code.