Geodesic
A quadratic part of a bent function can be any
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 342-347

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Boolean functions in $n$ variables that are on the maximal possible Hamming distance from all affine Boolean functions in $n$ variables are called bent functions ($n$ is even). They are intensively studied since sixties of XX century in relation to applications in cryptography and discrete mathematics. Often, bent functions are represented in their algebraic normal form (ANF). It is well known that the linear part of ANF of a bent function can be arbitrary. In this note we prove that a quadratic part of a bent function can be arbitrary too.
Keywords: Boolean function, bent function, linear function, quadratic function, homogeneous function. 
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N. N. Tokareva. A quadratic part of a bent function can be any. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 342-347. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a19/