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Definition D5931
Boolean parity function

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

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

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