Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes

Cardinality spectra of components of correlation immune functions, bent functions, perfect... 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 ∈ {0, ..., 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S003294601201005X
Publisher site
See Article on Publisher Site

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 ∈ {0, ..., 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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 17, 2012

References

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