As I recall, various types of error checking do better jobs of
detecting various types of errors (and, of course, error correcting codes
can correct up to a certain number of errors in the packet, then just
detect errors, then just give up).  In another project I did about 15
years ago, I was sending packets that were variable length, but often up
to 32 bytes.  I originally included an 8 bit checksum.  Errors would
occasionally get through undetetected.  Since the 8 bit checksum only has
256 possible values, it SEEMS there is a 1 in 256 possibility of an
erroneous packet getting through the checksum.  I then tried increasing
the checksum to 16 bits, but the sum of all the bytes rarely got to
anywhere near such a big number.  The method I settled upon involved
doing a left shift of the existing checksum value, then adding in the new
byte.  This was repeated  each time a byte was added to the packet.
Overflow was discarded.  Now that I think about it, perhaps discarding
overflow resulted in discarding error checking on the first bytes in the
packet, but the system vastly improved operation.
        by the way, this was a networked system based on audio links
between sites (which could be hundreds of miles away) using Bell 202 half
duplex modems.  It used a minislotted access method where each site was
allocated 50 mS to bring up carrier and start transmission if it had any
traffic.  If it did not have any traffic, it just left its carrier off
and all sites advanced their "site counter" to the next site that was
authorized to transmit.  Site counters were advanced 50 mS after
receiving the last byte, and every 50 mS thereafter.  During reception,
site counter advances were held off.  Thus the 50 mS "minislot" was
expanded into a "slot" that was large enough to handle whatever traffic
this site had.  Further, to keep the site counters in sync, each site
fully demodulated all traffic.  On receiving a valid packet from a site,
it was assumed that this site was indeed authorized to transmit at this
time, so the site counter was loaded with the address of the originating
site.  This insured that when the traffic ended, all sites incremented
their site counters to the same number, all authorizing the same site to
transmit.  the protocol handled up to 100 sites, though the largest
installation I know of is 15 or 20 sites.  Part of the setup of the
system is to put in the highest site number.  The boxes then reset their
site counters after that number is reached so they don't allocate time to
nonexistant sites.

Harold