Binary Codes Formed by Functions with Nontrivial Inertia Groups

Binary Codes Formed by Functions with Nontrivial Inertia Groups Let K be a permutation group acting on binary vectors of length n and F K be a code of length 2 n consisting of all binary functions with nontrivial inertia group in K. We obtain upper and lower bounds on the covering radii of F K , where K are certain subgroups of the affine permutation group GA n . We also obtain estimates for distances between F K and almost all functions in n variables as n → ∞. We prove the existence of functions with the trivial inertia group in GA n for all n ≥ 7. An upper bound for the asymmetry of a k-uniform hypergraph is obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Binary Codes Formed by Functions with Nontrivial Inertia Groups

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1013875401571
Publisher site
See Article on Publisher Site

Abstract

Let K be a permutation group acting on binary vectors of length n and F K be a code of length 2 n consisting of all binary functions with nontrivial inertia group in K. We obtain upper and lower bounds on the covering radii of F K , where K are certain subgroups of the affine permutation group GA n . We also obtain estimates for distances between F K and almost all functions in n variables as n → ∞. We prove the existence of functions with the trivial inertia group in GA n for all n ≥ 7. An upper bound for the asymmetry of a k-uniform hypergraph is obtained.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 9, 2004

References

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