What are convolutional codes 

Hamming distance is a measure of the difference between two strings of equal length. It quantifies the number of positions at which the corresponding symbols differ. In the context of binary strings or code words, it indicates how many bit positions need to be changed to convert one string into the other.

### Key Points:

- **Definition**: The Hamming distance between two strings is the number of positions where the corresponding bits are different. For example, the Hamming distance between the binary strings `101010` and `100100` is 2, because the strings differ at two positions.

- **Application**:

  - **Error Detection and Correction**: Hamming distance is used to evaluate the error-correcting capabilities of codes. For instance, a code with a minimum Hamming distance of \(d\) can detect up to \(d-1\) errors and correct up to \(\left\lfloor \frac{d-1}{2} \right\rfloor\) errors.

  - **Genetics and Information Theory**: The concept is used in fields like genetics to measure genetic variation and in information theory to assess the reliability of coding schemes.

In summary, Hamming distance is a key concept in information theory and coding that measures how different two strings are by counting the number of differing positions.