New Binomial Bent Functions Over the Finite Fields of Odd Characteristic
Tor Helleseth, Alexander Kholosha · IEEE Transactions on Information Theory · 2010
Thep-ary functionf(x) mappingGF(p4k) toGF(p) and given byf(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.