<s>
In	O
coding	B-Error_Name
theory	I-Error_Name
,	O
rank	O
codes	O
(	O
also	O
called	O
Gabidulin	B-Error_Name
codes	I-Error_Name
)	O
are	O
non-binary	O
linear	O
error-correcting	B-Error_Name
codes	I-Error_Name
over	O
not	O
Hamming	O
but	O
rank	O
metric	O
.	O
</s>
<s>
By	O
adding	O
redundancy	O
with	O
coding	O
k-symbol	O
word	O
to	O
a	O
n-symbol	O
word	O
,	O
a	O
rank	B-Error_Name
code	I-Error_Name
can	O
correct	O
any	O
errors	O
of	O
rank	O
up	O
to	O
t	O
=⌊(	O
d1	O
)	O
/2	O
⌋	O
,	O
where	O
d	O
is	O
a	O
code	O
distance	O
.	O
</s>
<s>
A	O
rank	B-Error_Name
code	I-Error_Name
is	O
an	O
algebraic	O
linear	O
code	O
over	O
the	O
finite	O
field	O
similar	O
to	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
code	I-Error_Name
.	O
</s>
<s>
The	O
rank	B-Error_Name
code	I-Error_Name
corrects	O
all	O
errors	O
with	O
rank	O
of	O
the	O
error	O
vector	O
not	O
greater	O
thant	O
.	O
</s>
<s>
The	O
easiest	O
one	O
to	O
construct	O
is	O
known	O
as	O
the	O
(	O
generalized	O
)	O
Gabidulin	B-Error_Name
code	I-Error_Name
,	O
it	O
was	O
discovered	O
first	O
by	O
Delsarte	O
(	O
who	O
called	O
it	O
a	O
Singleton	O
system	O
)	O
and	O
later	O
by	O
Gabidulin	O
(	O
and	O
Kshevetskiy	O
)	O
.	O
</s>
