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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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What error occurs if the number of bits is not an odd number for odd parity or an even parity?
parity error
What does ecc mean?
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.
Why to check odd or even parity?
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2.
How do you check orthogonality of a matrix using arrays?
the transpose of null space of A is equal to orthogonal complement of A
What is difference between parity checker and parity generator?
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.
