On the Existence of Agievich-Primitive Partitions

Tarannikov, Yuriy

doi:10.1134/s1990478922040202

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2023

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(2 citation statements)

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“…The same definition was proposed by Agievich [1], under the name primitivity, and was dubbed A-primitivity by Tarannikov [28]. We remark that an avsp A of AG(n, q) is tight iff for any x ∈ F n q , there exists an A ∈ A such that A is not invariant under addition of x, that is A + x = A.…”

Section: Definitionmentioning

confidence: 81%

“…A more general partition problem for groups is studied in [10]. Irreducible homogeneous affine vector space partitions have been studied by Agievich [1] and Tarannikov [28] motivated by the study of bent functions. However, we are not aware of any publication treating the introduced affine vector space partitions in the same generality as in the present work.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Affine vector space partitions

Bamberg

Filmus

Ihringer

et al. 2023

Des. Codes Cryptogr.

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An affine vector space partition of $${{\,\textrm{AG}\,}}(n,q)$$ AG ( n , q ) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.

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Section: Definitionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%