Reason behind the name **PARITY CHECK MATRIX**

Question

It is easy to understand the name Generator matrix because it generates a code C. But why the name Parity Check matrix ? i.e, I want to know the actual reason behind the name Parity check (because of behind every name there is a reason).

Answer 1

A simple check to ensure some binary string hasn't been corrupted is to add the digits using $1+1=0$ and checking to see if it sums to zero or one. This will catch one-off errors and is typically called a parity check. The parity check matrix does this as well and so is named a parity check matrix.