<s>
In	O
coding	B-Error_Name
theory	I-Error_Name
,	O
a	O
coset	B-Error_Name
leader	I-Error_Name
is	O
a	O
word	O
of	O
minimum	O
weight	O
in	O
any	O
particular	O
coset	O
-	O
that	O
is	O
,	O
a	O
word	O
with	O
the	O
lowest	O
amount	O
of	O
non-zero	O
entries	O
.	O
</s>
<s>
Sometimes	O
there	O
are	O
several	O
words	O
of	O
equal	O
minimum	O
weight	O
in	O
a	O
coset	O
,	O
and	O
in	O
that	O
case	O
,	O
any	O
one	O
of	O
those	O
words	O
may	O
be	O
chosen	O
to	O
be	O
the	O
coset	B-Error_Name
leader	I-Error_Name
.	O
</s>
<s>
Coset	B-Error_Name
leaders	I-Error_Name
are	O
used	O
in	O
the	O
construction	O
of	O
a	O
standard	O
array	O
for	O
a	O
linear	O
code	O
,	O
which	O
can	O
then	O
be	O
used	O
to	O
decode	O
received	O
vectors	O
.	O
</s>
<s>
For	O
a	O
received	O
vector	O
y	O
,	O
the	O
decoded	O
message	O
is	O
y	O
-	O
e	O
,	O
where	O
e	O
is	O
the	O
coset	B-Error_Name
leader	I-Error_Name
of	O
y	O
.	O
Coset	B-Error_Name
leaders	I-Error_Name
can	O
also	O
be	O
used	O
to	O
construct	O
a	O
fast	O
decoding	O
strategy	O
.	O
</s>
<s>
For	O
each	O
coset	B-Error_Name
leader	I-Error_Name
u	O
we	O
calculate	O
the	O
syndrome	O
uH′	O
.	O
</s>
<s>
The	O
corresponding	O
coset	B-Error_Name
leader	I-Error_Name
is	O
the	O
most	O
likely	O
error	O
pattern	O
and	O
we	O
assume	O
that	O
v+u	O
was	O
the	O
codeword	O
sent	O
.	O
</s>
