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Construction of cubic homogeneous Boolean bent functions [PDF]

Australas. J Comb., 2000
Summary: The authors prove that cubic homogeneous bent functions \(f:V_{2n}\to GF(2)\) exist for all \(n\geq 3\) except for \(n=4\).
Seberry, Jennifer, Xia, Tianbing, Pieprzyk, J. +2 more
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Cubic bent functions outside the completed Maiorana-McFarland class [PDF]

Designs, Codes, and Cryptography, 2020
In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana- McFarland construction does not describe the whole class of cubic bent functions in n variables for all n ≥ 10.
Alexandr Polujan, Alexander Pott, Pott Alexander +2 more
exaly +2 more sources

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Homogeneous Bent Functions, Invariants, and Designs

Designs, Codes and Cryptography, 2002
Bent functions are special polynomial functions over the 2-element Boolean ring. They have been studied extensively for the last 30 years and play an important role in coding theory and cryptography. In this paper, the authors present new methods of constructing homogeneous bent functions.
Charnes, C., Roetteler, Martin, Beth, Thomas +2 more
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On the Nonexistence of Homogeneous Rotation Symmetric Bent Boolean Functions of Degree Greater Than Two

2008
In this paper we present a result towards the conjectured nonexistence of homogeneous rotation symmetric bent functions having degree >2.
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On the conjecture about the nonexistence of homogeneous rotation symmetric bent functions