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.
Problems of Information Transmission – Springer Journals
Published: Oct 9, 2004
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