What does $\mathbb{Z}_2^3$ mean? Is the subscript $2$ a modulo and the superscript $3$ dimensions of each element? I am studying lattice cryptography and set theory and I would like to know the how the LWE works in the simplest way possible.
Here’s what I have found from a research paper:
It somewhat depends, but generally $\mathbb{Z}_2$ will mean either the integers mod $2$ (i.e. $\mathbb{Z}/2\mathbb{Z}$) or (less likely in your case) the $2$-adic numbers. The superscript $3$ will generally mean the Cartesian product. Hence, $$\begin{align*} \mathbb{Z}_2^3 &= \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2 \\ &= \{ (x,y,z) \mid x,y,z \in \mathbb{Z}_2 \} \end{align*}$$