Algorithm Issue: letter combinations

Question

I'm trying to write a piece of code that will do the following:

Take the numbers 0 to 9 and assign one or more letters to this number. For example:

0 = N,
1 = L,
2 = T,
3 = D,
4 = R,
5 = V or F,
6 = B or P,
7 = Z,
8 = H or CH or J,
9 = G

When I have a code like 0123, it's an easy job to encode it. It will obviously make up the code NLTD. When a number like 5,6 or 8 is introduced, things get different. A number like 051 would result in more than one possibility:

NVL and NFL

It should be obvious that this gets even "worse" with longer numbers that include several digits like 5,6 or 8.

Being pretty bad at mathematics, I have not yet been able to come up with a decent solution that will allow me to feed the program a bunch of numbers and have it spit out all the possible letter combinations. So I'd love some help with it, 'cause I can't seem to figure it out. Dug up some information about permutations and combinations, but no luck.

Thanks for any suggestions/clues. The language I need to write the code in is PHP, but any general hints would be highly appreciated.

Update:

Some more background: (and thanks a lot for the quick responses!)

The idea behind my question is to build a script that will help people to easily convert numbers they want to remember to words that are far more easily remembered. This is sometimes referred to as "pseudo-numerology".

I want the script to give me all the possible combinations that are then held against a database of stripped words. These stripped words just come from a dictionary and have all the letters I mentioned in my question stripped out of them. That way, the number to be encoded can usually easily be related to a one or more database records. And when that happens, you end up with a list of words that you can use to remember the number you wanted to remember.

Answer 1

It can be done easily recursively.

The idea is that to handle the whole code of size n, you must handle first the n - 1 digits. Once you have all answers for n-1 digits, the answers for the whole are deduced by appending to them the correct(s) char(s) for the last one.