network-programmingcommunicationparityhamming-code

Horizontal and Vertical Parity check codes

I was reading about horizontal and vertical parity check codes. One of the properties of these codes is that the final parity check (the lower right bit) is equal to modulo 2 sum of horizontal parity checks and also equal to modulo 2 of sum of vertical parity checks.

I did not understand, why this is true. I can see them in the examples but i really cant come up with any formal/intuitive proof about the same.

Any help/hints will be appreciated.

Thanks, Chander

Solution

  • Each row and column is sum modulo 2. And result is sum of all numbers mod 2. It does not matter how you count.

    Rule is:
    ((a mod c) + (b mod c)) mod c == (a+b) mod c