Difficulty in understanding the definition of this sequence

Discussion in 'Mathematics' started by I_wil_break_wall, Oct 8, 2018.

1. I_wil_break_wallGuest

Let $G$ be a finite group and $J=\langle g_1,\cdots g_k\rangle$ be a sequence of group elements. For any $\delta \ge 1$, $J$ is said to be a cube generating sequence for $G$ with closeness parameter $\delta$, if the probability distribution $D_J$ on $G$ given by $g_1^{\epsilon_1}\cdots g_k^{\epsilon_k},$ where each $\epsilon_i$ is independent and uniformally distributed in {0,1}, is $\delta$-close to the uniform distribution in the $L_2$ norm.

Question: What is the difference between ordinary generating set and generating set given abobve?