Please indent your code correctly, that would help you see some of your errors or suboptimal loops. Also use the strict and warnings pragmas, this would also help you.

How about this:

use strict;
use warnings;

my @files = qw / NC_002755.fq NC_009525.fq NC_009565.fq NC_012943.fq N
+C_016768.fq NC_016934.fq NC_017026.fq NC_017522.fq NC_017523.fq NC_01
+7524.fq NC_017528.fq NC_018078.fq NC_018143.fq NC_020089.fq /;
@files = map {s/\.fq$//; $_} @files;
while (my $seq = <DATA>) {
    my @seq = split /\s+/, $seq;
    printf "%-50s", "@seq[0..1] ";
    my %found_files = map { s/\.\w+$// ; $_ => 1} grep {/NC_/} @seq[2.
+.$#seq];
    for my $file (@files) {
        print exists $found_files{$file} ? "1\t" : "0\t"
    }
    print "\n";
}

__DATA__
(3R)-hydroxyacyl-ACP dehydratase subunit HadA    NC_021192.1
(3R)-hydroxyacyl-ACP dehydratase subunit HadB    NC_017026.1
(dimethylallyl)adenosine tRNA methylthiotransferase    NC_009565.1    
+NC_002755.2    NC_009525.1    NC_016934.1
1,4-alpha-glucan branching protein    NC_021192.1    NC_017522.1    NC
+_016934.1    NC_018078.1    NC_020089.1    NC_002755.2    NC_017524.1
+    NC_009565.1    NC_012943.1    NC_017523.1    NC_021740.1
1,4-dihydroxy-2-naphthoate octaprenyltransferase    NC_016934.1    NC_
+017026.1    NC_009525.1
1,4-dihydroxy-2-naphthoyl-CoA synthase    NC_018143.2    NC_009565.1  
+  NC_002755.2    NC_012943.1    NC_017523.1
[download]

Which prints this:

$ perl fq_files.pl
(3R)-hydroxyacyl-ACP dehydratase                  0     0       0     
+  0       0       0       0       0       0       0       0       0  
+     0       0
(3R)-hydroxyacyl-ACP dehydratase                  0     0       0     
+  0       0       0       1       0       0       0       0       0  
+     0       0
(dimethylallyl)adenosine tRNA                     1     1       1     
+  0       0       1       0       0       0       0       0       0  
+     0       0
1,4-alpha-glucan branching                        1     0       1     
+  1       0       1       0       1       1       1       0       1  
+     0       1
1,4-dihydroxy-2-naphthoate octaprenyltransferase  0     1       0     
+  0       0       1       1       0       0       0       0       0  
+     0       0
1,4-dihydroxy-2-naphthoyl-CoA synthase            1     0       1     
+  1       0       0       0       0       1       0       0       0  
+     1       0
[download]