Under the condition that at most one x with χ(x)=χ(x+1)=1 satisfies (x+1)^r - x^r = b for each b, the binomial F_r(x) = x^r + x^{r+(q-1)/2} is locally-APN with boomerang uniformity ≤2 over F_q (q≡3 mod 4), plus spectra for F_3, F_{(2q-1)/3} and F_2 (p=3).
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Locally-APN Binomials with Low Boomerang Uniformity in Odd Characteristic
Under the condition that at most one x with χ(x)=χ(x+1)=1 satisfies (x+1)^r - x^r = b for each b, the binomial F_r(x) = x^r + x^{r+(q-1)/2} is locally-APN with boomerang uniformity ≤2 over F_q (q≡3 mod 4), plus spectra for F_3, F_{(2q-1)/3} and F_2 (p=3).