| Title: | Vectorial negabent concepts : similarities, differences, and generalizations |
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| Authors: | ID Anbar, Nurdagül (Author)
ID Kudin, Sadmir (Author)
ID Meidl, Wilfried (Author)
ID Pašalić, Enes (Author)
ID Polujan, Alexandr (Author) |
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| Files: |  RAZ_Anbar_Nurdagul_2025.pdf (450,92 KB)
MD5: DB9AD21DB1498E3E5635A0FD5B1EBA2F
 https://link.springer.com/article/10.1007/s10623-024-01454-2
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | 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 Fn 2 to the cyclic group Z2k . It is shown how to obtain nega-Z2k -bent functions from Z2k -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 Z8 -bent functions employing per- mutations with the (Am ) property, and more generally we show that the inverse permutation gives rise to Z2k -bent functions. |
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| Keywords: | bent function, Maiorana-McFarland class, negabent functions |
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| Publication date: | 05.07.2024 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 899-921 |
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| Numbering: | Vol. 93, iss. 4 |
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| PID: | 20.500.12556/RUP-21722  |
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| UDC: | 510.633.3 |
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| ISSN on article: | 0925-1022 |
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| DOI: | 10.1007/s10623-024-01454-2 |
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| COBISS.SI-ID: | 207993347 |
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| Publication date in RUP: | 12.09.2025 |
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| Views: | 365 |
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| Downloads: | 12 |
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