On certain values of Kloosterman sums
IEEE Transactions on Information Theory
Proofs of two conjectures on ternary weakly regular bent functions
IEEE Transactions on Information Theory
On the dual of monomial quadratic p-ary bent functions
SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Strongly regular graphs associated with ternary bent functions
Journal of Combinatorial Theory Series A
On integer values of Kloosterman sums
IEEE Transactions on Information Theory
New binomial bent functions over the finite fields of odd characteristic
IEEE Transactions on Information Theory
Ternary Kloosterman sums modulo 18 using Stickelberger's theorem
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Sequences, Bent functions and Jacobsthal sums
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Designs, Codes and Cryptography
Association schemes arising from bent functions
Designs, Codes and Cryptography
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
On the dual of a Coulter--Matthews bent function
Finite Fields and Their Applications
Weil sums of binomials, three-level cross-correlation, and a conjecture of Helleseth
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
New three-valued walsh transforms from decimations of helleseth-gong sequences
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
A construction of bent functions from plateaued functions
Designs, Codes and Cryptography
| Hi-index | 755.08 |
Considered are p-ary bent functions having the form f(x)=Trn(σi=0saixdi). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.