Anbar Meidl, Nurdagül and Kalaycı, Tekgül and Meidl, Wilfried (2026) Twisted partial difference sets, twisted LP-packings and bent partitions. Designs, Codes, and Cryptography, 94 (6). ISSN 0925-1022 (Print) 1573-7586 (Online)
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Official URL: https://dx.doi.org/10.1007/s10623-026-01886-y
Abstract
Recently, the first constructions of bent partitions of elementary abelian groups that do not induce partial difference sets or Latin square type partial difference set packings (LP-packings) have been presented (Anbar et al.; Wang et al., 2025). Motivated by observations on the differential properties of examples of these bent partitions, the notions of twisted partial difference sets and twisted LP-packings in abelian groups G are introduced in this article. Basic properties of twisted partial difference sets and twisted LP-packings, as well as properties of the corresponding character values, are investigated. It is shown that the sets arising from all recently introduced bent partitions are twisted partial difference sets, and that these bent partitions induce twisted LP-packings. As a consequence, all nontrivial bent partitions of elementary abelian groups known so far are shown to correspond either to LP-packings or to twisted LP-packings.
| Item Type: | Article |
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| Additional Information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Uncontrolled Keywords: | (Twisted) LP-packings; (Twisted) partial difference sets; Bent functions; Bent partitions; Vectorial bent functions |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Nurdagül Anbar Meidl |
| Date Deposited: | 16 Jun 2026 13:04 |
| Last Modified: | 16 Jun 2026 13:04 |
| URI: | https://research.sabanciuniv.edu/id/eprint/54172 |
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