Biembeddings of small order hamming STS(n) and APN monomial power permutations

Josep Rifa, Faina I. Solov'Eva, Merce Villanueva

Research output: Chapter in BookChapterResearchpeer-review


The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n = 2m - 1 for small m (m ≤ 22), is given. For m J{5, 7,11,13,17,19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m. 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 proposed. This classification for APN monomial power permutations coincides with the CCZ-equivalence, at least up to m ≤ 17.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Number of pages5
Publication statusPublished - 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


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