I have a few questions here that I hope you's can help me with:

1) Does a binary (8,4,5) code exist?

2)Does a binary (7,3,5) code exist?

(n,M,d) - n length of codeword, M size of code, d is the minimum distance.

3) Determine whteher or not the following subsets are supspaces of (i)Z^4 3 and (ii) [B]Z[B]^4 5 respectively.

(i) S = {x=x1x2x3x4: x1=X3 & x2=x4}

(ii) S = {x=x1x2x3x4: x1=1}

Looking forward to some replys!