It’s not shortness that counts, it’s matching closely what you intend the code to mean. Your original code is not very good because you don’t mean “check if it’s between 6 and 20 letters, numbers and underscores, but make sure it has no underscores.” You mean “check that it’s between 6 and 20 letters and numbers,” so that’s what the code should do:

print( ( $s =~ m{ \A [[:alnum:]]{6,20} \z }x ) ? "success" : "invalid 
+string" );
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Makeshifts last the longest.