# Do I need to use a matrix of size N x n for the public key in the BGV scheme when using Ring-LWE?

I'm going through the BGV paper and trying to make a toy implementation, but I just want to focus on Ring-LWE. In the paper, they set $$N = \lceil{(2n + 1)\log_2(q)\rceil}$$, and generate $$A'$$ uniformly from $$R_q^{N\times{n}}$$. From what I can tell, they do this because they focus on the GLWE problem. While reading some other papers(such as the standard paper from homomorphicencryption.org), I notice they seem just sample from $$R_q$$ instead of $$R_q^{N\times{n}}$$.

Is it necessary to sample from $$R_q^{N\times{n}}$$, or is it sufficient to just sample from $$R_q$$? If the latter, why does BGV suggest the former?

BGV Paper