Suppose that $y$ is a uniform random variable that is defined over the field (or group or abelian group) $Y$. Let us suppose that there are $N=\{1,2,\cdots,i\cdots,N\}$ agents and only one of them, say $i$, knows the random variable $y$. She wants to share the secret with the other $|N|-1$ players. So we could assume that player $i$ could find $x_1,x_2,\cdots,x_{K}$, where $K=|N|-1$, i.i.d uniform random variables over the space $Y$ and $a_1,a_2,...,a_k$ non_zero constants such that the $$\sum_{j\neq i}^Na_jx_j=y?$$
So every player $j=-i$ would know the part a_jx_j and only if all of them make a cross communication and calculate $a_1x_1\oplus_Ya_2x_2\oplus_Y\cdots\oplus_Ya_kx_k$ then all together will learn $y$. Could this be a secret sharing scheme, where the uniform random variable $Y$ could be written as a linear combination of a family of i.i.d. uniform random vectors that also belong to $Y$?
If my idea is not how could someone enrich it so as to become complete and a multiparty computation will need to be applied so as the players would obtain the secret $y$ only if they contribute all of them their private information that they got from the agent $i$?
What could be the weakness of such a scheme and how could we confront it? Does this have bounds?
P.S. i dont know if it is necessary to write the calculation in the following way
$$(a_1\otimes_Yx_1)\oplus_Y(a_2\otimes_Yx_2)\oplus_Y\cdots\oplus_Y(a_k\otimes_Yx_k)$$