Abstract: The properties of maximal prefix codes are established in this paper. We prove that tho family of maximal prefix codes forms a free monoid under the language concatenation, operation.
A recurrence formula for tho number of finite maximal prefix codes is given as follows:
Let G_m denote the number of maximal prefix codes in which the length of words is equal to m or less than it, we have then
G_m=1+G_m-1ⁿ
Where n is the number of letters of alphabet X.