## Parity Check code

Can only detect **one** error and cannot correct any errors

## Repetition Code

Can correct

$$\bigg\lfloor \dfrac{n-1}{2} \bigg\rfloor$$

errors

and can detect $n-1$ errors

## Hamming distance

Measures the number of differences (in this case 1)

The **Hamming weight** is the number of non zeroes (2 for top, 1 for bottom)

## Minimum distance

A code can correct t errors iff it has a minimum distance

$$d_{min}\geqslant 2t+1$$

So for this code it can correct 1 error (min distance of 3 would also work to correct 1 error)

There needs to be overlap between the codes in order to be able to distinguish them

As the $d_{min}$ is an integer value, the formula is equivalent to $d_{min}>2t$