## Basic definitions

Enough examples - now for the definition.

Definition 3.3.3   Let be a finite field. A subset of is called a code of length . A subspace of is called a linear code of length . If then is called a binary code. If then is called a ternary code. If has elements then is called a -ary code. The elements of a code are called code words or code vectors. Sometimes elements of which do not necessarily belong to are called received vectors''.

The information rate of is

where denotes the number of elements of .

david joyner 2008-04-20