Self-embeddings of Hamming Steiner triple systems of small order and APN permutations
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Solov'eva, Faina I. (Sobolev Institute of Mathematics)
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date:	2015
Abstract:	The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n = 2 m − 1 for small m (m ≤ 22), is given. As far as we know, for m ∈ {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.
Grants:	Ministerio de Ciencia e Innovación MTM2009-08435 Ministerio de Ciencia e Innovación TIN2010-17358 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	APN functions ; Hamming codes ; Self-embeddings ; Steiner triple systems
Published in:	Designs, codes and cryptography, Vol. 75 Issue 3 (June 2015) , p. 405-427, ISSN 1573-7586

DOI: 10.1007/s10623-013-9909-1

Post-print 24 p, 809.3 KB

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