Recall that a code C is a subset of S^n, where S is a fixed, finite alphabet and S^n denotes the set of all strings of length n over S. Recall also that the hamming distance between two n-length strings u and v over S is the number of indicies on which u and v differ, and d(C) denotes the smallest hamming distance between any pair of strings in C. Finally, a code C is said to correct t errors if for every u \in S^n there is at most one w \in C such that d(u,w) \leq t.
Now consider the following statement.
A code C corrects d errors if and only if: d(C) \geq {\color{red}{\star}}.
What is {\color{red}\star}?
