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## nt.quantity concept – Polynomials in $mathbb F_3[x_1,dots,x_{kt}]$ offering $i$th little bit of addition of $t$ integers certain in magnitude by $2^okay$

Define $mathsf{MultipleAddition}(a_1,dots,a_t,i)$ breathe the $i$th little bit of $a_1,dots,a_n$ and occupy $t=mathsf{poly}(n)$ and occupy $okay=lceillog_2(max(|a_1|,dots,|a_t|))rceil=mathsf{poly}(n)$.

At each $iin{1,dots,kt}$ are there $r=mathsf{poly}(n)$ polynomials $g_1,dots,g_rinmathbb F_3[x_1,dots,x_{kt}]$ having diploma $O(log(n))$ polynomial having $O(mathsf{poly}(n))$ monomials satisfying

$$mathsf{MultipleAddition}(a_1,dots,a_t,i)=immense(sum_{i=1}^rg_i(mathsf{int2bin}(a_1,dots,a_t))immense)bmod 2$$

the place $mathsf{int2bin}$ binarizes the $t$ integers offering $kt$ binary digits?

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