Short of going to a completely different hash implementation, there are incremental improvements you can make to improve your code... You can factor out the indexing operations: Instead of

if (      ($genome[$i] eq 'a') 
       && ($genome[$i+1] eq 'a')) { ++$tt; }
elsif (   ($genome[$i] eq 'a') 
       && ($genome[$i+1] eq 'g')) { ++$ag; }
elsif (   ($genome[$i] eq 'a') 
       && ($genome[$i+1] eq 'c')) { ++$ac; }
elsif (   ($genome[$i] eq 'a') 
       && ($genome[$i+1] eq 't')) { ++$at; }
elsif (   ($genome[$i] eq 't') 
       && ($genome[$i+1] eq 'a')) { ++$ta; }

...
[download]

use...

my $genome =   $genome[$i];
my $genome1 =  $genome[$i+1];

if (      ($genome eq 'a') 
       && ($genome1 eq 'a')) { ++$tt; }
elsif (   ($genome eq 'a') 
       && ($genome1 eq 'g')) { ++$ag; }
elsif (   ($genome eq 'a') 
       && ($genome1 eq 'c')) { ++$ac; }
elsif (   ($genome eq 'a') 
       && ($genome1 eq 't')) { ++$at; }
elsif (   ($genome eq 't') 
       && ($genome1 eq 'a')) { ++$ta; }

...
[download]

Finding the array elements is done only once, rather than once per comparison. The next improvement would be to concatenate the two elements and halve the number of comparisons try...

my $genomepair =   $genome[$i] . $genome[$i+1];

if (      $genomepair eq 'aa' ) { ++$tt; }
elsif (   $genomepair eq 'ag')  { ++$ag; }
elsif (   $genomepair eq 'ac')  { ++$ac; }
elsif (   $genomepair eq 'at')  { ++$at; }
elsif (   $genomepair eq 'ta')  { ++$ta; }

...
[download]

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