Some t-Homogeneous Sets of Permutations

Authors:
Jürgen Bierbrauer;Stephen Black;Yves Edel
Affiliations:
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931 (USA);IBM Heidelberg (Germany) Mathematisches Institut der Universität, Im Neuenheimer Feld 288, 69120 Heidelberg (Germany);Mathematisches Institut der Universität, Im Neuenheimer Feld 288, 69120 Heidelberg (Germany)
Venue:
Designs, Codes and Cryptography - Special issue containing papers presented at the Second Upper Michigan Combinatorics Workshop on Designs, Codes and Geometries
Year:
1996

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Abstract

Perpendicular Arrays are orderedcombinatorial structures, which recently have found applicationsin cryptography. A fundamental construction uses as ingredientscombinatorial designs and uniformly t-homogeneoussets of permutations. We study the latter type of objects. Thesemay also be viewed as generalizations of t-homogeneousgroups of permutations. Several construction techniques are given.Here we concentrate on the optimal case, where the number ofpermutations attains the lower bound. We obtain several new optimalsuch sets of permutations. Each example allows the constructionof infinite families of perpendicular arrays.