<s>
In	O
general	O
,	O
computation	B-Algorithm
of	I-Algorithm
CRC	I-Algorithm
corresponds	O
to	O
Euclidean	O
division	O
of	O
polynomials	O
over	O
GF(2 )	O
:	O
</s>
<s>
The	O
CRC	O
'	O
checksum	B-Algorithm
 '	O
is	O
formed	O
by	O
the	O
coefficients	O
of	O
the	O
remainder	O
polynomial	O
whose	O
degree	O
is	O
strictly	O
less	O
than	O
.	O
</s>
<s>
In	O
practice	O
CRC	O
calculations	O
most	O
closely	O
resemble	O
long	B-Algorithm
division	I-Algorithm
in	O
binary	O
,	O
except	O
that	O
the	O
subtractions	O
involved	O
do	O
not	O
borrow	O
from	O
more	O
significant	O
digits	O
,	O
and	O
thus	O
become	O
exclusive	O
or	O
operations	O
.	O
</s>
<s>
A	O
CRC	O
is	O
a	O
checksum	B-Algorithm
in	O
a	O
strict	O
mathematical	O
sense	O
,	O
as	O
it	O
can	O
be	O
expressed	O
as	O
the	O
weighted	O
modulo-2	O
sum	O
of	O
per-bit	O
syndromes	O
,	O
but	O
that	O
word	O
is	O
generally	O
reserved	O
more	O
specifically	O
for	O
sums	O
computed	O
using	O
larger	O
moduli	O
,	O
such	O
as	O
10	O
,	O
256	O
,	O
or	O
65535	O
.	O
</s>
<s>
CRCs	O
can	O
also	O
be	O
used	O
as	O
part	O
of	O
error-correcting	B-Error_Name
codes	I-Error_Name
,	O
which	O
allow	O
not	O
only	O
the	O
detection	O
of	O
transmission	O
errors	O
,	O
but	O
the	O
reconstruction	O
of	O
the	O
correct	O
message	O
.	O
</s>
<s>
2-bit	O
errors	O
in	O
a	O
(	O
multiple	O
)	O
distance	O
of	O
the	O
longest	O
bitfilter	O
of	O
even	B-Error_Name
parity	I-Error_Name
to	O
a	O
generator	O
polynomial	O
are	O
not	O
detected	O
;	O
all	O
others	O
are	O
detected	O
.	O
</s>
