TY - JOUR
T1 - Intersection of Hamming codes avoiding Hamming subcodes
AU - Rifà, J.
AU - Soloveva, F. I.
AU - Villanueva, M.
PY - 2012/1/1
Y1 - 2012/1/1
N2 - 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.
AB - 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.
KW - APN functions
KW - Cryptography
KW - Hamming codes
KW - Intersection of Hamming codes
KW - Projective geometries
U2 - 10.1007/s10623-011-9506-0
DO - 10.1007/s10623-011-9506-0
M3 - Article
SN - 0925-1022
VL - 62
SP - 209
EP - 223
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2
ER -