A note on difference families from cyclotomy

Explicit Constructions of Perfect Hash Families from Algebraic Curves over Finite Fields

Two types of permutation polynomials with special forms

The p-ary function f(x) mapping GF(p4k) to GF(p) and given by f(x)=Tr4k(xp3k+p2k-pk+1+x2) is proven to be a weakly regular bent function and the exact value of its Walsh transform coefficients is found. This is the first proven infinite class of nonquadratic generalized bent functions over the fields of an arbitrary odd characteristic. The proof is based on a few new results in the area of exponential sums and polynomials over finite fields that may also be interesting as independent problems.

On the support varieties of tilting modules

We consider the boomerang uniformity of an infinite class of (locally-APN) power maps and show that their boomerang uniformity over the finite field $$\mathbb {F}_{2^n}$$ is 2 and 4, when $$n \equiv 0 \pmod 4$$ and $$n \equiv 2 \pmod 4$$ , respectively. As a consequence, we show that for this class of power maps, the differential uniformity is strictly greater than their boomerang uniformity.

Difference families from rings