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Problemy Peredachi Informatsii, 2012, Volume 48, Issue 1, Pages 54–63
(Mi ppi2068)
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This article is cited in 17 scientific papers (total in 17 papers)
Coding Theory
Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes
V. N. Potapovab a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk
Abstract:
We study cardinalities of components of perfect codes and colorings, correlation immune functions, and bent function (sets of ones of these functions). Based on results of Kasami and Tokura, we show that for any of these combinatorial objects the component cardinality in the interval from $2^k$ to $2^{k+1}$ can only take values of the form $2^{k+1}-2^p$, where$p\in\{0,\dots,k\}$ and $2^k$ is the minimum component cardinality for a combinatorial object with the same parameters. For bent functions, we prove existence of components of any cardinality in this spectrum. For perfect colorings with certain parameters and for correlation immune functions, we find components of some of the above-given cardinalities.
Received: 15.04.2011 Revised: 02.11.2011
Citation:
V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Probl. Peredachi Inf., 48:1 (2012), 54–63; Problems Inform. Transmission, 48:1 (2012), 47–55
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https://www.mathnet.ru/eng/ppi2068 https://www.mathnet.ru/eng/ppi/v48/i1/p54
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Abstract page: | 435 | Full-text PDF : | 84 | References: | 50 | First page: | 11 |
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