Generalized semifield spreads

Anbar, Nurdagül; Kalaycı, Tekgül; Meidl, Wilfried

doi:10.1007/s10623-022-01115-2

Des. Codes Cryptogr.

2022

DOI: 10.1007/s10623-022-01115-2

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Generalized semifield spreads

Nurdagül Anbar

Tekgül Kalaycı

Wilfried Meidl

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Cited by 10 publications

References 13 publications

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Vectorial negabent concepts: similarities, differences, and generalizations

Anbar,

Kudin,

Meidl

et al. 2024

Des. Codes Cryptogr.

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In Pasalic et al. (IEEE Trans Inf Theory 69:2702–2712, 2023), and in Anbar and Meidl (Cryptogr Commun 10:235–249, 2018), two different vectorial negabent and vectorial bent-negabent concepts are introduced, which leads to seemingly contradictory results. One of the main motivations for this article is to clarify the differences and similarities between these two concepts. Moreover, the negabent concept is extended to generalized Boolean functions from $${\mathbb {F}}_2^n$$ F 2 n to the cyclic group $${\mathbb {Z}}_{2^k}$$ Z 2 k . It is shown how to obtain nega-$${\mathbb {Z}}_{2^k}$$ Z 2 k -bent functions from $${\mathbb {Z}}_{2^k}$$ Z 2 k -bent functions, or equivalently, corresponding non-splitting relative difference sets from the splitting relative difference sets. This generalizes the shifting results for Boolean bent and negabent functions. We finally point to constructions of $${\mathbb {Z}}_8$$ Z 8 -bent functions employing permutations with the $$({\mathcal {A}}_m)$$ ( A m ) property, and more generally we show that the inverse permutation gives rise to $${\mathbb {Z}}_{2^k}$$ Z 2 k -bent functions.

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Vectorial negabent concepts: similarities, differences, and generalizations

Anbar,

Kudin,

Meidl

et al. 2024

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

On generalized spread bent partitions

Anbar,

Kalaycı,

Meidl

2023

Cryptogr. Commun.

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Amorphic association schemes from bent partitions

Anbar,

Kalaycı,

Meidl

2024

Discrete Mathematics

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Generalized semifield spreads

Cited by 10 publications

References 13 publications

Vectorial negabent concepts: similarities, differences, and generalizations

Vectorial negabent concepts: similarities, differences, and generalizations

On generalized spread bent partitions

Amorphic association schemes from bent partitions

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