A note on the FMEI of the Boolean functions in the Generalized Maiorana-McFarland construction.
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| Title: | A note on the FMEI of the Boolean functions in the Generalized Maiorana-McFarland construction. |
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| Authors: | Li, Zhaole1 (AUTHOR) lizhaole@sjtu.edu.cn, Tang, Deng1 (AUTHOR) dtang@foxmail.com |
| Source: | Discrete Applied Mathematics. Jul2026, Vol. 387, p106-115. 10p. |
| Subjects: | Boolean functions, Bent functions, Uncertainty (Information theory) |
| Abstract: | This paper investigates well-known conjectures in Boolean function analysis, specifically focusing on the Fourier Min-Entropy/Influence (FMEI) conjecture, a natural relaxation of the more established Fourier Entropy/Influence (FEI) conjecture. While the FEI conjecture proposes that the Fourier entropy of a Boolean function is bounded by a constant multiple of its total influence, the FMEI conjecture substitutes entropy with min-entropy. We present a construction of Boolean functions that establishes a new lower bound on the universal constant of the FMEI conjecture. By employing the Generalized Maiorana-McFarland construction with suitably chosen injective mappings, we construct Boolean functions whose FMEI value surpasses the previous bound 2.8444. Specifically, our construction can yield functions demonstrating an FMEI value strictly less than 4 but arbitrarily close to 4, and we provide the conditions for the FMEI value to exceed 3. Furthermore, we investigate other classes of plateaued functions, such as partially bent functions and the Address functions, and prove that relaxing the injective constraint in the Generalized Maiorana-McFarland construction cannot increase the FMEI value. Thereby, it provides new insights toward understanding of the FMEI conjecture. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193089973 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A note on the FMEI of the Boolean functions in the Generalized Maiorana-McFarland construction. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Zhaole%22">Li, Zhaole</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lizhaole@sjtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Tang%2C+Deng%22">Tang, Deng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dtang@foxmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jul2026, Vol. 387, p106-115. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Bent+functions%22">Bent functions</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates well-known conjectures in Boolean function analysis, specifically focusing on the Fourier Min-Entropy/Influence (FMEI) conjecture, a natural relaxation of the more established Fourier Entropy/Influence (FEI) conjecture. While the FEI conjecture proposes that the Fourier entropy of a Boolean function is bounded by a constant multiple of its total influence, the FMEI conjecture substitutes entropy with min-entropy. We present a construction of Boolean functions that establishes a new lower bound on the universal constant of the FMEI conjecture. By employing the Generalized Maiorana-McFarland construction with suitably chosen injective mappings, we construct Boolean functions whose FMEI value surpasses the previous bound 2.8444. Specifically, our construction can yield functions demonstrating an FMEI value strictly less than 4 but arbitrarily close to 4, and we provide the conditions for the FMEI value to exceed 3. Furthermore, we investigate other classes of plateaued functions, such as partially bent functions and the Address functions, and prove that relaxing the injective constraint in the Generalized Maiorana-McFarland construction cannot increase the FMEI value. Thereby, it provides new insights toward understanding of the FMEI conjecture. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.02.052 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 106 Subjects: – SubjectFull: Boolean functions Type: general – SubjectFull: Bent functions Type: general – SubjectFull: Uncertainty (Information theory) Type: general Titles: – TitleFull: A note on the FMEI of the Boolean functions in the Generalized Maiorana-McFarland construction. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Zhaole – PersonEntity: Name: NameFull: Tang, Deng IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 387 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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