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Дискретная математика и математическая кибернетика
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
Аннотация:
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.
Ключевые слова:
Boolean function, bent function, linear function, quadratic function, homogeneous function.
Поступила 13 марта 2022 г., опубликована 29 июня 2022 г.
Образец цитирования:
N. N. Tokareva, “A quadratic part of a bent function can be any”, Сиб. электрон. матем. изв., 19:1 (2022), 342–347
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1505 https://www.mathnet.ru/rus/semr/v19/i1/p342
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