MHB Show that the codeword a cannot be a valid codeword.

[Reyawakens]

Let d=d1d2d3d4d5d6d7 be a valid codeword of Hamming (7,4) code. Suppose a=a1a2a3a4a5a6a7 be another codeword that differs from d precisely at two bits. Show that the codeword a cannot be a valid codeword.

May I ask how to solve this type of problem?

 

[romsek]

what's the Hamming distance of the (7,4) code? (hint: it's 3)

Can a valid codeword exist at a Hamming distance of 2 bits in a code with a Hamming distance of 3?