On minimal distance between q-ary bent functions

Potapov, Vladimir N.

doi:10.1109/red.2016.7779341

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Observe that every potential bent function f obtained from is either a bent function obtained from (if f takes on the same value on U and on A 1 ), or a function that differs from a bent function obtained from solely on the subspace U by a constant. Hence, by Proposition 1 in [18] for p = 2, and the analog result for odd p in [31], the function f is bent as well. Therefore is a normal bent partition.…”

Section: A K } If and Only If A 1 Contains An N/2-dimensional Subspace Umentioning

confidence: 68%

“…n → F p is at least p n/2 , see [17], Proposition 1 in [18], and [31] for odd p (and even n). Exchanging two sets A j 1 and A j 2 in the preimages of c 1 and c 2 we get two bent functions f , g with distance…”

Section: Lemma 1 Let P Be An Odd Prime and Fmentioning

confidence: 99%

“…By the definition of a normal bent partition we can obtain bent functions f , g which only differ on the set U of cardinality p n/2 . Then f and g have the minimal possible distance between bent functions, and U must be an affine subspace of V ( p) n , see [17], Proposition 1 in [18], and [31] for odd p.…”

Section: Remarkmentioning

confidence: 99%

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Bent partitions

Anbar

Meidl

2022

Des. Codes Cryptogr.

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Spread and partial spread constructions are the most powerful bent function constructions. A large variety of bent functions from a 2m-dimensional vector space V ( p) 2m over F p into F p can be generated, which are constant on the sets of a partition of V ( p) 2m obtained with the subspaces of the (partial) spread. Moreover, from spreads one obtains not only bent functions between elementary abelian groups, but bent functions from V ( p) 2m to B, where B can be any abelian group of order p k , k ≤ m. As recently shown (Meidl, Pirsic 2021), partitions from spreads are not the only partitions of V(2) 2m , with these remarkable properties. In this article we present first such partitions-other than (partial) spreads-which we call bent partitions, for V ( p) 2m , p odd. We investigate general properties of bent partitions, like number and cardinality of the subsets of the partition. We show that with bent partitions we can construct bent functions from V ( p) 2m into a cyclic group Z p k . With these results, we obtain the first constructions of bent functions from V ( p) 2m into Z p k , p odd, which provably do not come from (partial) spreads.

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Section: A K } If and Only If A 1 Contains An N/2-dimensional Subspace Umentioning

confidence: 68%