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 ) .
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