Hamming distance and error detection/correction properties

Let's assume I want to have a possibility of detecting 4-bit errors and recovering 2-bit errors. What the Hamming distan开发者_如何学运维ce should be then?

I wonder if it should be d = Max{2r+1, r+1} or d = s + r, where s is 4 and r is 2?

Thanks in advance for the reply!

Cheers

ed + ec <= dmin -1
ed = 4
ec = 2

therefore

dmin >= 4 + 2 + 1 = 7

and Hamming distance (t) is

t = 1/2(dmin - 1) = 3

d=Max(2*r+1,s+1)

is correct.

so the answer is 5.

When you have a minimum hamming distance of length 5 you can detect at max only 4 bit errors because if there is a 5 bit error then the codeword (obtained by having error) is a valid codeword because minimum hamming distance is 5 so insertion of 5 bit error causes conversion of valid codeword to another valid codeword.