# use an all-perl approach:
opendir( DIR, "." );
@files = sort {$b cmp $a} grep /BC.*?\.txt$/, readdir DIR;
close DIR;

open( OUT, ">BCfile.name" );
for ( grep !/Liver/, @files ) {
  s/\..*/\n/;
  print OUT;
}
close OUT;

# OR... a little bit of reliance on a sub-shell is okay too;
# the next four lines do the same thing just as well:

@files = map {s/\..*//; $_} grep !/Liver/, `ls -r *BC*.txt`;
open  OUT, ">BCfile.name";
print OUT join "", @files;
close OUT;