The boolean parity function with respect to $N \in 1, 2, 3, \ldots$ is the D218: Boolean function \begin{equation} \{ 0, 1 \}^N \to \{ 0, 1 \}, \quad x \mapsto I_{2 \mathbb{Z} + 1} \left( \sum_{n = 1}^N x_n \right) \end{equation}

The boolean parity function with respect to $N \in 1, 2, 3, \ldots$ is the D218: Boolean function \begin{equation} \{ 0, 1 \}^N \to \{ 0, 1 \}, \quad x \mapsto I_{\sum_{n = 1}^N x_n \in 2 \mathbb{Z} + 1} \end{equation}

The boolean parity function with respect to $N \in 1, 2, 3, \ldots$ is the D218: Boolean function \begin{equation} \{ 0, 1 \}^N \to \{ 0, 1 \}, \quad x \mapsto \begin{cases} 1, \quad & \sum_{n = 1}^N x_n \text{ is odd} \\ 0, \quad & \text{otherwise} \\ \end{cases} \end{equation}