We prove that given a binary Hamming code Hn of length n = 2 m - 1, m ≥ 3, or equivalently a projective geometry PG(m - 1, 2), there exist permutations π ∈ Sn, such that Hn and Hn 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. © 2011 Springer Science+Business Media, LLC.
|Journal||Designs, Codes, and Cryptography|
|Publication status||Published - 1 Jan 2012|
- APN functions
- Hamming codes
- Intersection of Hamming codes
- Projective geometries