Given binary sequences of equal length, let the "distance" between them be defined as the number of bits that would need to be flipped to convert one binary sequence to another. For example, the sequences 1111 and 1110 are a distance of 1 apart, because only the last digit must be changed to get from one to the other. Meanwhile, 1010 and 0101 are a distance of 4 apart, because all 4 digits must be changed to get from one to the other.
Consider binary sequences of length 8 (example: 10101010). Is it possible to find a group of 5 of them such that each is a distance of at least 5 from all the others? If so, give an example of such a group, thus producing a successful 5 x 8 grid. If not, prove that it is not possible to find any such group and that therefore the 5 x 8 grid cannot be filled.