|
Discrete mathematics and mathematical cybernetics
A quadratic part of a bent function can be any
N. N. Tokarevaab a Sobolev Institute of Mathematics, 4, Koptyuga, ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pyrogova str., Novosibirsk, 630090, Russia
Abstract:
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.
Received March 13, 2022, published June 29, 2022
Citation:
N. N. Tokareva, “A quadratic part of a bent function can be any”, Sib. Èlektron. Mat. Izv., 19:1 (2022), 342–347
Linking options:
https://www.mathnet.ru/eng/semr1505 https://www.mathnet.ru/eng/semr/v19/i1/p342
|
Statistics & downloads: |
Abstract page: | 124 | Full-text PDF : | 45 | References: | 31 |
|