Geodesic
On plateaued Boolean functions with the same spectrum support
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1346-1368

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In the first half of the paper we give a brief review of plateaued functions, regular functions and related topics including connections with problems on subgraphs of the Hamming graph. In the second half of the paper we discover wide infinite families of spectrum supports for which it is possible to count the number of plateaued Boolean functions with such spectrum supports and give corresponding formulas; only one infinite sequence of such spectrum supports was known before.
Keywords: plateaued functions, Boolean functions, Walsh Spectrum, Fourier spectrum, spectrum support, spectral analysis, regular functions, correlation immune functions, $m$-resilient functions, address function, recursive constructions, Hamming graph, regular graphs, symmetries.
Mots-clés : spectra, equitable partitions 
@article{SEMR_2016_13_a67,
     author = {A. V. Khalyavin and M. S. Lobanov and Yu. V. Tarannikov},
     title = {On plateaued {Boolean} functions with the same spectrum support},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1346--1368},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a67/}
}
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A. V. Khalyavin; M. S. Lobanov; Yu. V. Tarannikov. On plateaued Boolean functions with the same spectrum support. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1346-1368. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a67/