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Página principal > Artículos > Artículos publicados > Self-embeddings of Hamming Steiner triple systems of small order and APN permutations |
Fecha: | 2015 |
Resumen: | 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. |
Ayudas: | 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 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | APN functions ; Hamming codes ; Self-embeddings ; Steiner triple systems |
Publicado en: | Designs, codes and cryptography, Vol. 75 Issue 3 (June 2015) , p. 405-427, ISSN 1573-7586 |
Post-print 24 p, 809.3 KB |