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Error Detection (1bit and 2 bit):

Error Detection (1 bit):

Corrupted Code: Corrupted should not be valid, otherwise error can’t be detected. Therefore, in order to detect 1 bit error, the distance between two valid patterns (code) should be at least 2 (two).

Example 1:

We are using a code where pattern used as

We can’t use this code pattern because the distance between two valid codes is 1 here.

So, if there is one-bit error at 0000, it might be changed to 0001. So, it is valid we can’t detect the error.

Example 2:

So, here every two valid pattern distance is 2. Therefore, we can use it to detect the 1-bit error.

So, if there is a 1-bit error at 0000 then it might be

So, no code is a valid pattern because it is not listed above, so, all are invalid and we easily detect 1-bit error.

Error detection (2-bit error):

There free in order to detect the 2-bit error. The distance between two valid codes (pattern) should be at least 3 (three).

For 3 bit error, the distance between two valid codes is definitely 4.

So,

So, for n bit error then definitely the minimum distance between two valid code ≥ n + 1.

# This distance between every two valid codes is called Hamming Distance of the code.

# So, for n bit error hamming distance between two code always ≥ n + 1.