What is the minimum number of bits needed to correct all 2 bit errors? -

i learned hamming codes , how use them correct 1 bit errors , detect 2 bit errors, how extend correcting 2 bits, , maybe more?

what minimum number of bits needed correct 2 bit errors?

i think figured out.

n=number of data bits, k=number error correcting bits(eg parity hamming)

in ecc scheme, have 2^(n+k) possible bit strings.

for single bit error:

you must find k such total number of possible bit strings larger possible number of strings @ 1 bit error given string.

the total possible strings @ 1 bit error 2^n(n+k+1)

1 string no error, n+k strings 1 bit error

2^(n+k)>=(2^n)*(n+k+1)

you have plugin values of k until find 1 satisfies above(or wish solve it)

similarly 2 bit error, is

1 string no error, n+k strings 1 bit error, n+k choose 2 strings 2 bit error.

2^(n+k)>=(2^n)*(n+k+1 + (n+k choose 2))