TY - JOUR
T1 - Self-embeddings of Hamming Steiner triple systems of small order and APN permutations
AU - Rifà, Josep
AU - Solov’eva, Faina I.
AU - Villanueva, Mercè
PY - 2015/6/1
Y1 - 2015/6/1
N2 - © 2014, Springer Science+Business Media New York. The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of ordern n = 2m-1 for small m (m≤22), is given. As far as we know, for m ε {5,7,11,13,17,19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m and nonorientable at least for all m≤19. For any non prime m, the nonexistence of such self-embeddings in a closed surface is proven. The rotation line spectrum for self-embeddings of Hamming Steiner triple systems in pseudosurfaces with pinch points as an invariant to distinguish APN permutations or, in general, to classify permutations, is also proposed. This invariant applied to APN monomial power permutations gives a classification which coincides with the classification of such permutations via CCZ-equivalence, at least up to m≤17.
AB - © 2014, Springer Science+Business Media New York. The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of ordern n = 2m-1 for small m (m≤22), is given. As far as we know, for m ε {5,7,11,13,17,19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m and nonorientable at least for all m≤19. For any non prime m, the nonexistence of such self-embeddings in a closed surface is proven. The rotation line spectrum for self-embeddings of Hamming Steiner triple systems in pseudosurfaces with pinch points as an invariant to distinguish APN permutations or, in general, to classify permutations, is also proposed. This invariant applied to APN monomial power permutations gives a classification which coincides with the classification of such permutations via CCZ-equivalence, at least up to m≤17.
KW - APN functions
KW - Hamming codes
KW - Self-embeddings
KW - Steiner triple systems
U2 - 10.1007/s10623-013-9909-1
DO - 10.1007/s10623-013-9909-1
M3 - Article
SN - 0925-1022
VL - 75
SP - 405
EP - 427
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
ER -