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 Prikl. Diskr. Mat. Suppl., 2015, Issue 8, Pages 39–43 (Mi pdma235)

Discrete Functions

Properties of $p$-ary bent functions that are at minimal distance from each other

V. N. Potapov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: It is proved that, in the case of prime $p$, the minimal Hamming distance between distinct $p$-ary bent functions in $2n$ variables is equal to $p^n$. It is shown that for $p>2$ the number of $p$-ary bent functions being on the minimal distance from a quadratic bent function is equal to $p^n(p^{n-1}+1)\cdots(p+1)(p-1)$.

Keywords: bent function, Hamming distance, quadratic form.

DOI: https://doi.org/10.17223/2226308X/8/16

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UDC: 519.7

Citation: V. N. Potapov, “Properties of $p$-ary bent functions that are at minimal distance from each other”, Prikl. Diskr. Mat. Suppl., 2015, no. 8, 39–43

Citation in format AMSBIB
\Bibitem{Pot15} \by V.~N.~Potapov \paper Properties of $p$-ary bent functions that are at minimal distance from each other \jour Prikl. Diskr. Mat. Suppl. \yr 2015 \issue 8 \pages 39--43 \mathnet{http://mi.mathnet.ru/pdma235} \crossref{https://doi.org/10.17223/2226308X/8/16}