TY - CHAP

T1 - Biembeddings of small order hamming STS(n) and APN monomial power permutations

AU - Rifa, Josep

AU - Solov'Eva, Faina I.

AU - Villanueva, Merce

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84890418574&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2013.6620350

DO - 10.1109/ISIT.2013.6620350

M3 - Chapter

AN - SCOPUS:84890418574

SN - 9781479904464

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 869

EP - 873

BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013

ER -