# Tag Info

$\mathbf{Z}_2^b$ is the direct product of $b$ copies of $\mathbf{Z}_2$ ($\mathbf{Z}_2 \times\cdots \times \mathbf{Z}_2$, $b$ times). That is, its elements are $b$-tuples of elements of $\mathbf{Z}_2$, with both addition and multiplication defined componentwise. If $b > 1$, it is not a field. In fact it is not even an integral domain, because $(0,1)\times ... 1 We can present$\mathbb{Z}_m$in different manner. For example, bellow sets are some equivalence classes of$\mathbb{Z}_3$$$\{0,1,2\}, \{3,4,5\},\{-3,-2,-1\}.$$ Now, about your question If you select the numbers of$[-n,n]$module a positive integer$m$which$m\leq 2n+1$, you can construct$\mathbb{Z}_m\$: $$\mathbb{Z}_m=\{i \pmod m \mid i\in[-n,n]\}$$ ...