Paul, I hope this isn't homework.

The quickest way I've found to do a CRC-32 (not a CRC-16, sorry, but it'll work fine for checking files) is to use Compress::Zlib's crc32 function:

use Compress::Zlib;
my $crc32 = 0;
while (<>)
{
 $crc32 = Compress::Zlib::crc32($_, $crc32);
}
print "CRC is $crc32\n";
[download]

Perhaps this will help you. There is also Digest::MD5, and a simple checksum available using Perl's builtin unpack.