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