With a little tidying (to my eye anyway) and applying suggestions from imp and BrowserUK the following code gives the same answers as the original for the small range of values I've tested and ought to be somewhat faster.

#!c:\perl\bin\perl

use strict;
use warnings;


my %index_val = ( A=> 2,
                  C => 3,
                  D => 4,
                  N => 2,
                  M => 2,
                  T => 1,
                  G => 4);

my $sequence="ACTGACN";
my $distance_index = 2;
my $window = 2;

my $arr_ref = &alpha_index({ sequence => $sequence,
                           distance => $distance_index,    
                           aa_index => \%index_val,
                           window_size => $window });

for my $hashRef (@$arr_ref) {
    print join "\n", map {"$_ => $hashRef->{$_}"} keys %$hashRef;
    print "\n";
}


sub alpha_index {
    my $self=shift;
    my $sequence=$self->{sequence};
    my $distance=$self->{distance};
    my $aa_index=$self->{aa_index};
    my @carbon_index;
    my $window_size = int $self->{window_size};

    $window_size = int ($window_size - 1) / 2 if $window_size > 1;

    foreach my $len (0 .. (length($sequence)-1)) {
        my %carbon_aa;
        my ($left, $middle, $right) = splitStr ($sequence, $len);
        $carbon_aa{$middle} = $aa_index->{$middle} if $middle;
        $left = reverse $left;

        my $initial_index = 2;
        my $length_index= $window_size ? $window_size : length $left;

        if($self->{window_size} == 1 ) {
            push @carbon_index, \%carbon_aa if %carbon_aa;
            next;
        }

        foreach my $increment (0 .. $length_index-1) {
            my $left_aa=substr($left,$increment,1);
            next if not exists $aa_index->{$left_aa};
            
            my $distance_index= $initial_index ** $distance;
            
            $carbon_aa{$middle} += $aa_index->{$left_aa} * (1/$distanc
+e_index);
            $initial_index++;
        }
        
        $initial_index=2;
        $length_index= $window_size ? $window_size : length $right;
        
        foreach my $increment (0 .. $length_index-1) {
            my $right_aa=substr ($right, $increment, 1);
            next if not exists $aa_index->{$right_aa};
            
            my $distance_index= $initial_index ** $distance;
            
            $carbon_aa{$middle} += $aa_index->{$right_aa} * (1 / $dist
+ance_index);
            $initial_index++;
        }
        
        push @carbon_index, \%carbon_aa if %carbon_aa;
    }

    return \@carbon_index;
}


sub splitStr {
    return (
        substr($_[0], 0, $_[1]),
        substr($_[0], $_[1], 1),
        substr($_[0], $_[1] + 1)
        );
}
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