The Hilton-Milner type results of $(k,\ell )$-sum-free sets in ${\mathbb{F}}_p^n$

Xin Wei, Xiande Zhang, Gennian Ge

For a prime $p\equiv 2(\mathrm{mod}3)$, it is well known that the largest sum-free subsets of ${\mathbb{F}}_p^n$ have size $\frac{p+1}{3}{p}^{n-1}$, and the extremal sets must be a cuboid o…