If I understand what you want right (you want to find a subsequences of a large string that are equal to a given set of strings of length 32), and your alphabet has a reasonable size (letters, digits and punctuation, for instance), then you can do the following:
Find the first occurrence of each letter.
For each position in the string, find the next occurrence of every letter after this position (you can do it in O(l * n)
where l is the length of the string and n is the size of your alphabet by scanning from the end for each letter)
For each string in your set of strings, find the first occurrence of the first letter of that string, then from that position find the first occurrence of the second letter in your string etc.
This way you spend O(l * n)
time to preprocess, but then for each small string in your set you only do O(m)
work where m is the length of that string.