# Producing a binary string that has maximum distance to a set of binary strings

Suppose I have a set of $d$-length binary strings $S = \{0,1\}^{k\times d}$. How can construct a new string of $d$-length so that the minimum hamming distance w.r.t. the strings in $S$ is maximized?

• Does $S$ have any special structure, e.g. is it a linear code? – Batman Apr 3 '15 at 14:23
• No structures. Maybe the assumption that $2^d >> k$. – Adam I. Apr 3 '15 at 14:43