
## Structure of a hamming code

![Structure of a hamming code](/img/Uni/CaC/ECC/hamming_structure.png)

This H is the **parity check matrix**

### Properties

| Property                    | Value         |
| --------------------------- | ------------- |
| Length                      | $2^r-1$       |
| Dimension                   | $2^r-r-1$     |
| Minimum distance            | 3             |
| Field order                 | 2             |
| Redundancy                  | $r-k$         |
| Rate                        | $1-r/(2^r-1)$ |
| Error correction capability | 1             |

From the parity check matrix, you can then form the Generator matrix

![Hamming code generator matrix](/img/Uni/CaC/ECC/hamming_generator.png)


Hamming Codes

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notes

Property	Value
Length	$$2^r-1$$
Dimension	$$2^r-r-1$$
Minimum distance	3
Field order	2
Redundancy	$$r-k$$
Rate	$$1-r/(2^r-1)$$
Error correction capability	1