Since that you are checking first and last characters with $b[$i-($m-1)] and $b[$i] respectively, your in-between characters should be

@b[$i-($m-2)..$i-1]
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That is,
say

$i = 10;
$m = 8;
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Your first character according to your check should be in $b[3] and last character should be in $b[10]. So the in-between characters should be

@b[4..9]
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But you are checking 3..10 again.
From your code, for(my $j=($i-($m-1));$j<=$i;$j++)
I guess this should be

for(my $j=($i-($m-2));$j<=$i-1;$j++)
#or
for(my $j=($i-($m-2));$j<$i;$j++)
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Does this help you.
Thanks..