Cryptography Reference
In-Depth Information
Figure 4.1 - Product code resulting from the serial concatenation of two systematic
block codes.
where
d
=
d
0
d
k−
1
represents the dataword.
d
1
···
The minimum
distance of this code is
2
.
Example 4.3
A generator matrix
G
of this code for
n
=5
,
k
=4
is equal to:
⎡
⎤
10001
01001
00101
00011
⎣
⎦
=
I
4
P
G
=
and the parity check matrix
H
is reduced to one vector.
H
=
11111
=
P
T
I
1
Repetition code
For this code with parameters
k
=1
and
n
=2
m
+1
, each bit coming from the
information source is repeated an odd number of times. The minimum distance
of this code is
2
m
+1
. The repetition code
C
(2
m
+1
,
1)
is the dual code of the
parity check code
C
(2
m
+1
,
2
m
)
.