Further to hippo's excellent comments, I would add with regard to

$dna       = <FASTQ>;
...;
$qual      = <FASTQ>;
@dna       = split ('', $dna);
@qual      = split ('', $qual);
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and similar from the tidied source that the code uses the same name for variables of different type. IMHO, it's not, in general, good practice to do this; eventually, you'll give yourself a terrible headache. Don't do that. In general, use informative, distinctive names for variables, subroutines, etc.