A few thougts:

1) Always use strict; use warnings; and declare your variables.

2) Think about the type of your variables. while ($stem gt $offset) seems pretty useless to me. I'd suspect $stem to be a string, $offset certainly is a number. Maybe you need while ($offset < length($stem) - 1){ ... }?

3) $dictionary{$dict} = $dict; are you sure you need exactly that? I'd somehow suspect that need to look up those digrams in the hash, but that won't work if you take the whole word as hash key.

I think you need to be more specific about what you try to achieve, and how you want to do it (I'm not familiar with dice's coefficient, and I'm sure I'm not the only one).