Abstract
We prove that given a binary Hamming code \({{\mathcal{H}}^n}\) of length n = 2m − 1, m ≥ 3, or equivalently a projective geometry PG(m − 1, 2), there exist permutations \({\pi \in \mathcal{S}_n}\) , such that \({{\mathcal{H}}^n}\) and \({\pi({\mathcal{H}}^n)}\) do not have any Hamming subcode with the same support, or equivalently the corresponding projective geometries do not have any common flat. The introduced permutations are called AF permutations. We study some properties of these permutations and their relation with the well known APN functions.
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Communicated by S. Ball.
An erratum to this article is available at http://dx.doi.org/10.1007/s10623-014-0011-0.
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Rifà, J., Solov’eva, F.I. & Villanueva, M. Intersection of Hamming codes avoiding Hamming subcodes. Des. Codes Cryptogr. 62, 209–223 (2012). https://doi.org/10.1007/s10623-011-9506-0
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DOI: https://doi.org/10.1007/s10623-011-9506-0