Strongly regular graphs associated with ternary bent functions
Journal of Combinatorial Theory Series A
New families of almost perfect nonlinear power mappings
IEEE Transactions on Information Theory
Monomial and quadratic bent functions over the finite fields of odd characteristic
IEEE Transactions on Information Theory
p-Ary and q-ary versions of certain results about bent functions and resilient functions
Finite Fields and Their Applications
Sequences, Bent functions and Jacobsthal sums
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Strongly regular graphs constructed from p-ary bent functions
Journal of Algebraic Combinatorics: An International Journal
Crosscorrelation of m-sequences, exponential sums, bent functions and Jacobsthal sums
Cryptography and Communications
A construction of weakly and non-weakly regular bent functions
Journal of Combinatorial Theory Series A
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
On generalized bent functions with Dillon's exponents
Information Processing Letters
| Hi-index | 754.84 |
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.