Proofs of two conjectures on ternary weakly regular bent functions

Authors:
Tor Helleseth;Henk D. L. Hollmann;Alexander Kholosha;Zeying Wang;Qing Xiang
Affiliations:
Selmer Center, Department of Informatics, University of Bergen, Bergen, Norway;Philips Research Laboratories, AE, Eindhoven, The Netherlands;Selmer Center, Department of Informatics, University of Bergen, Bergen, Norway;Department of Mathematicals, Ohio University, Athens, OH;Department of Mathematicals, Ohio University, Athens, OH
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 13
Cited 4

Planar Functions and Planes of Lenz-Barlotti Class II

Designs, Codes and Cryptography
Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets

Journal of Combinatorial Theory Series A
Nonlinear functions in abelian groups and relative difference sets

Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Highly nonlinear mappings

Journal of Complexity - Special issue on coding and cryptography
A Note on the Proof of Niho's Conjecture

SIAM Journal on Discrete Mathematics
Skew Hadamard difference sets from the Ree--Tits slice symplectic spreads in PG(3,32h+1)

Journal of Combinatorial Theory Series A
Pseudo-Paley graphs and skew Hadamard difference sets from presemifields

Designs, Codes and Cryptography
On the dual of monomial quadratic p-ary bent functions

SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Monomial and quadratic bent functions over the finite fields of odd characteristic

IEEE Transactions on Information Theory
Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications

IEEE Transactions on Information Theory
On the dual of a Coulter--Matthews bent function

Finite Fields and Their Applications
p-Ary and q-ary versions of certain results about bent functions and resilient functions

Finite Fields and Their Applications
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences

Finite Fields and Their Applications

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
Sequences and functions derived from projective planes and their difference sets

WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields

Quantified Score

Hi-index	754.84

Visualization

Abstract

In this paper, we study ternary monomial functions of the form f(x) = Trn(axd), where x ∈ F3n and Trn: F3n → F3 is the absolute trace function. Using a lemma of Hou, Stickelberger's theorem on Gauss sums, and certain ternary weight inequalities, we show that certain ternary monomial functions arising in the 2006 IEEE TRANSACTIONS ON INFORMATION THEORY paper (vol. 52, pp. 2018-2032, 2006) are weakly regular bent, thus settling a conjecture of Helleseth and Kholosha. We also prove that the Coulter-Matthews bent functions are weakly regular.