Instead of reading in the whole file and using substr(), you might want to use seek and read to read in just the part of the file you're interested in:

my $bytepos = shift || die "must supply bytepos";

my $offset  = 4;

my $startpos = $bytepos - $offset;
$startpos = 0 if $startpos < 0;

seek(F, $startpos, 0) or die "Can't seek: $!";

read(F, $chunk, $offset * 2) or die "Can't read: $!";
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This will be a big win on especially large files.