In order to generate the parity check matrix you must first have the generator matrix and the codeword to check and see if it is correct.
1. Place your generator in row reduction form
2. Get the basis vectors
3. Put the vectors together to get the parity check matrix
4. Check it b multiplying the codewords by the parity = 0
For an example: 2*4 Generator Matrix
[1 0 1 1
0 1 1 0]
Rank = 2...therefore the number of columns is 2...Rank + X = # of columns of the Generator matrix
v1+v3+v4 = 0
v2+v3 = 0
v1 = -r1-r2
v2 = -r1
v3 = r1
v4 = r2
Parity = [-1 -1
-1 0
1 0
0 1]
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parity error
ECC stands for "error correcting code". It is a way to check for accuracy by adding one bit of redundant data (or parity data) to the end of each byte. As an example, when the digits of a byte total an odd number, the parity bit will be a zero. When it is even, it will be a one. If the parity bits do not match their respective bytes, the data is known to be corrupted.
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.
the transpose of null space of A is equal to orthogonal complement of A
A parity generator checks the data to be transmitted and outputs a 0(parity bit) if the number of logic 1's in the data is even, and a logic 0 if the number is odd. So a checker takes the transmitted data and the parity bit and will compare the two, and if they are both of the same logic then the you can conclude that the data was recieved succesfully(i.e no bits were lost during transmission). Parity checker/generator use the exact same devices, but with one comparing instead of generating.