Efficient substring matching in perl

I am looking for an efficient solution to do find the longest possible substring in a string tolerating n mismatches in the main string

Eg: Main String

1. AGACGTACTACTCTACTAGATGCA*TACTCTAC*
2. AGACGTACTACTCTACTAGATGCA*TACTCTAC*
3. AGACGTACTACTCTACAAGATGCA*TACTCTAC*
4. AGACGTACTACTTTACAAGATGCA*TACTCTAC*

Search String:

1. TACTCTACT : this should be considered a match to all of the above main strings.

Also I there could be the case where part of the substring is at the end of main string and I would like to pick that up also.

I would appreciate if you could give some pointers.

PS: I will have one search string and about 100 million main strings to search the substring for.

Thanks! -Abhi

use strict;
use warnings;
use feature qw( say );

sub match {
   my ($s, $t, $max_x) = @_;

   my $m = my @s = unpack('(a)*', $s);
   my $n = my @t = unpack('(a)*', $t);

   my @length_at_k     = ( 0 ) x ($m+$n);
   my @mismatches_at_k = ( 0 ) x ($m+$n);
   my $offset = $m;

   my $best_length = 0;
   my @solutions;
   for my $i (0..$m-1) {
      --$offset;

      for my $j (0..$n-1) {
         my $k = $j + $offset;

         if ($s[$i] eq $t[$j]) {
            ++$length_at_k[$k];
         }
         elsif ($length_at_k[$k] > 0 && $mismatches_at_k[$k] < $max_x) {
            ++$length_at_k[$k];
            ++$mismatches_at_k[$k];
         }
         else {
            $length_at_k[$k] = 0;
            $mismatches_at_k[$k] = 0;
         }

         my $length = $length_at_k[$k] + $max_x - $mismatches_at_k[$k];
         $length = $i+1 if $length > $i+1;

         if ($length >= $best_length) {
            if ($length > $best_length) {
               $best_length = $length;
               @solutions = ();
            }

            push @solutions, $i-$length+1;
         }
      }
   }

   return map { substr($s, $_, $best_length) } @solutions;
}

say for match('AABBCC', 'DDBBEE', 2);

Output:

AABB
ABBC
BBCC