Combinatorial designs, difference sets and bent functions as perfect colorings of graphs and multigraphs

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作者：

Potapov, V.N.

Avgustinovich, S.V.

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Bent function - Combinatorial design - Delsarte-hoffman bound - Difference sets - Equitable partitions - Grassmann graph - Hyper graph - Johnson graph - Perfect colorings - Q-design - Transversal of hypergraph;

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引用

共 29 条

[21] Bent Functions, Partial Difference Sets, and Quasi-Frobenius Local Rings
Xiang-dong Hou
Designs, Codes and Cryptography, 2000, 20 : 251 - 268
[22] New results on vectorial dual-bent functions and partial difference sets
Wang, Jiaxin
Fu, Fang-Wei
DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (01) : 127 - 149
[23] New results on vectorial dual-bent functions and partial difference sets
Jiaxin Wang
Fang-Wei Fu
Designs, Codes and Cryptography, 2023, 91 (1) : 127 - 149
[24] Plateaued functions, partial geometric difference sets, and partial geometric designs
Xu, Bangteng
JOURNAL OF COMBINATORIAL DESIGNS, 2019, 27 (12) : 756 - 783
[25] Automorphisms and equivalence of bent functions and of difference sets in elementary Abelian 2-groups
Dempwolff, U
COMMUNICATIONS IN ALGEBRA, 2006, 34 (03) : 1077 - 1131
[26] Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions
Yu Qing Chen
John Polhill
Journal of Algebraic Combinatorics, 2013, 37 : 11 - 26
[27] Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions
Chen, Yu Qing
Polhill, John
JOURNAL OF ALGEBRAIC COMBINATORICS, 2013, 37 (01) : 11 - 26
[28] Solving NP-hard problems on GATEx graphs: Linear-time algorithms for perfect orderings, cliques, colorings, and independent sets
Hellmuth, Marc
Scholz, Guillaume E.
THEORETICAL COMPUTER SCIENCE, 2024, 1037
[29] Functions f from Fn p, n=2m, to Z pk for which the character sum Hk f (pt, u) = ∼ x.Fn p. ptf (x) pk. u. x p (where.q=e2pi/ q is a q-th root of unity), has absolute value pm for all u. Fn p and 0=t = k-1, induce relative difference sets in Fn p x Z pk hence are called bent. Functions only necessarily satisfying |Hk f (1, u)| = pm are called generalized bent. We show that with spreads we not only can construct a variety of bent and generalized bent functions, but also can design functions from Fn p to Zpm satisfying |Hm f (pt, u)| = pm if and only if t. T for any T. {0, 1..., m-1}. A generalized bent function can also be seen as a Boolean (p-ary) bent function together with a partition of Fn p with certain properties. We show that the functions from the completed Maiorana-McFarland class are bent functions, which allow the largest possible partitions.
Meidl, Wilfried
Pott, Alexander
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2019, 11 (06): : 1233 - 1245

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