Geodesic
Curvature of the Boolean majority function
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 155-165.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Boolean majority function and the generalized Boolean majority function of an even number $n$ of variables are considered. For these functions exact values of the Walsh coefficients and the curvature are calculated.
Keywords: Boolean majority function, Walsh coefficients, Boolean function curvature. 
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A. S. Tissin. Curvature of the Boolean majority function. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 155-165. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a10/

[1] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yaschenko V.V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2012, 584 pp.

[2] Logachev O. A., Fedorov S. N., Yashchenko V. V., “On the $\Delta$-equivalence of Boolean functions”, Discrete Math. Appl., 30:2 (2020), 93–101 | DOI | MR | Zbl

[3] Logachev O. A., Fedorov S. N., Yashchenko V. V., “Boolean functions as points on the hypersphere in the Euclidean space”, Discrete Math. Appl., 29:2 (2019), 89–101 | DOI | MR | MR | Zbl

[4] Kamlovskii O.V., “Summy modulei koeffitsientov Uolsha–Adamara nekotorykh sbalansirovannykh bulevykh funktsii”, Matematicheskie voprosy kriptografii, 19:2 (2017), 129–145

[5] de la Cruz Jimenez R. A., Kamlovskiy O. V., “The sum of modules of Walsh coefficients of Boolean functions”, Discrete Math. Appl., 26:5 (2016), 259–272 | MR | Zbl

[6] Dalai D.K., Maitra S., Sarkar S., “Basic theory in construction of Boolean functions with maximum possible annihilator immunity”, Designs, Codes and Cryptography, 40:1 (2006), 75–98 | DOI | MR

[7] Kuznetsov D.S., Spetsialnye funktsii, Vysshaya shkola, M., 1962, 249 pp.

[8] Ivchenko G.I., Medvedev Yu.I., Mironova V.A., “Mnogochleny Kravchuka i ikh primeneniya v zadachakh kriptografii i teorii kodirovaniya”, Matematicheskie voprosy kriptografii, 6:1 (2015), 33–56 | MR

[9] MacWilliams E. J., Sloane N. J. A., The Theory of Error-Correcting Codes, Parts I, II., North-Holland, Amsterdam, 1977 | MR | Zbl

[10] Titswort R.C., Correlation properties of cyclic sequences, Calif. Inst. Technol., 1962, 244 pp.

[11] Sveshnikov A.G., Tikhonov A.N., Teoriya funktsii kompleksnoi peremennoi, FIZMATLIT, M., 2004, 336 pp.

[12] The Mathematics Magazine, 34:3 (1961), 178