3 Sea \(p \equiv 3 \pmod{4}\) un primo. Para \(i, k \in \{0, 1, \dots, p-1\}\) , construya \(x_{i,k} \in \{0, 1\}\) que satisfaga: \[(a) \sum_{k=0}^{p-1} x_{i,k} = \frac{p+1}{2}, \quad i = 0, 1, \dots, p-1;\] \[(b) \text{For } i, j \in \{0, 1, \dots, p-1\}, i \neq j, \quad \sum_{k=0}^{p-1} |x_{i,k} - x_{j,k}| = \frac{p+1}{2}.\]