This can be achieved using an binary linear code.

Next we will show how to construct syndrome encoding based on this linear code.

It isn't a simple linear code; it has a temporal component.

This fact is the property of linear code.

It applies the same idea to the parity check matrix H of a linear code.

When using a linear code let the be the syndrome of .

We know that the linear code is defined using the generator matrix.

This fact is one of the properties of linear code.

Let be a linear code such that has distance greater than .

For binary linear codes, they belong to the same coset.