Generate A Random String With A Set of Banned Substrings

I want to generate a random string of a fixed length L. However, there is a set of "banned" substrings all of length b that cannot appear in the string. Is there a way to algorithmically generate this parent string?

Here is a small example:

I want a string that is 10 characters long -> XXXXXXXXXX The banned substrings are {'AA', 'CC', 'AD'} The string ABCDEFGHIJ is a valid string, but AABCDEFGHI is not.

For a small example it is relatively easy to randomly generate and then check the string, but as the set of banned substrings gets larger (or the length of the banned substrings gets smaller), the probability of randomly generating a valid string rapidly decreases.