<s>
In	O
abstract	O
algebra	O
,	O
the	O
Chien	B-Error_Name
search	I-Error_Name
,	O
named	O
after	O
Robert	O
Tienwen	O
Chien	O
,	O
is	O
a	O
fast	O
algorithm	O
for	O
determining	O
roots	O
of	O
polynomials	O
defined	O
over	O
a	O
finite	O
field	O
.	O
</s>
<s>
Chien	B-Error_Name
search	I-Error_Name
is	O
commonly	O
used	O
to	O
find	O
the	O
roots	O
of	O
error-locator	O
polynomials	O
encountered	O
in	O
decoding	O
Reed-Solomon	B-Error_Name
codes	I-Error_Name
and	O
BCH	O
codes	O
.	O
</s>
<s>
Chien	B-Error_Name
search	I-Error_Name
improves	O
upon	O
the	O
above	O
by	O
selecting	O
a	O
specific	O
order	O
for	O
the	O
non-zero	O
elements	O
.	O
</s>
<s>
Consequently	O
,	O
Chien	B-Error_Name
search	I-Error_Name
needs	O
only	O
multiplications	O
by	O
constants	O
and	O
additions	O
.	O
</s>
<s>
The	O
Chien	B-Error_Name
search	I-Error_Name
is	O
based	O
on	O
two	O
observations	O
:	O
</s>
