20.500.12556/RUP-21513 The algebraic characterization of M-subspaces of bent concatenations and its application Every Boolean bent function f can be written either as a concatenation f = f1|| f2 of two complementary semi-bent functions f1, f2; or as a concatenation f = f1|| f2|| f3|| f4 of four Boolean functions f1, f2, f3, f4, all of which are simultaneously bent, semi-bent, or 5-valued spectra-functions. In this context, it is essential to specify conditions for these bent concatenations so that f does (not) belong to the completed Maiorana-McFarland class M#. In this article, we resolve this question completely by providing the algebraic characterization of M-subspaces for the concatenation of the form f = f1|| f2 and f = f1|| f2|| f3|| f4, which allows us to estimate ind( f ), the linearity index of f, and consequently to establish the necessary and sufficient conditions so that f is outside M#. Based on these conditions, we propose several explicit and generic design methods of specifying bent functions outside M# in the special case when f = g||h||g||(h+1), where g and h are bent functions. Moreover, we show that it is possible to even decrease the linearity index of f = g||h||g||(h+1), compared to ind(g) and ind(h), if the largest dimension of a common M-subspace of g and h is small enough (less than min{ind(g), ind(h)} − 1). This also induces iterative methods of constructing bent functions outside M# with (controllable) low linearity index. Finally, we derive a lower bound on the 2-rank of f and show that this concatenation method can generate bent functions that are provably outside M# ∪ PS# ap. In difference to the approach of Weng et al. (2007) that uses the direct sum and a bent function g outside M#, our method employs g, h ∈ M# for the same purpose. bent function Maiorana-McFarland class M-subspaces ukrivljene funkcije Maiorana-McFarland razred M-podprostori true false true Angleški jezik Slovenski jezik Članek v reviji 2025-08-04 14:21:08 2025-08-04 14:21:09 2025-08-05 03:02:40 0000-00-00 00:00:00 2025 0 0 str. 3999-4011 no. 5 Vol. 71 May 2025 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-03-04 51 0018-9448 10.1109/TIT.2025.3547533 244763651 RAZ_Kudin_Sadmir_2025.pdf RAZ_Kudin_Sadmir_2025.pdf 1 44FA811FD1EC3875F81453B8F9995D8F 6acf811bd237377462e14b4ef518050665c9672daff6ccf76b39123b1748cb29 27fbed04-712e-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31281 https://ieeexplore.ieee.org/document/10909699 1 83a51bcd-712d-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31279 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0