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.
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References
J. Bierbrauer, The uniformly 3–homogeneous subsets of PGL 2(q), Journal of algebraic combinatorics, Vol. 4 (1995) pp. 99–102.
J. Bierbrauer and Y. Edel, Theory of perpendicular arrays, Journal of Combinatorial Designs, Vol. 6 (1994) pp. 375–406.
J. Bierbrauer and Y.Edel, Halving PSL 2(q), to appear in Journal of Geometry.
J. Bierbrauer and T. v. Tran, Halving PGL 2(2f), f odd: a Series of Cryptocodes, Designs, Codes and Cryptography, Vol. 1 (1991) pp. 141–148.
J. Bierbrauer, T. v. Tran, Some highly symmetric Authentication Perpendicular Arrays, Designs, Codes and Cryptography, Vol. 1 (1992) pp. 307–319.
E. S. Kramer, D. L. Kreher, R. Rees, and D. R. Stinson, On perpendicular arrays with t ≤ 3, Ars Combinatoria, Vol. 28 (1989) pp. 215–223.
C. R. Rao, Combinatorial Arrangements analogous to Orthogonal Arrays, Sankhya A, Vol. 23 (1961) pp. 283–286.
D. R. Stinson, The Combinatorics of Authentication and Secrecy Codes, Journal of Cryptology, Vol. 2 (1990) pp. 23–49.
D. R. Stinson and L. Teirlinck, A Construction for Authentication/Secrecy Codes from 3–homogeneous Permutation Groups, European Journal of Combinatorics, Vol. 11 (1990) pp. 73–79.
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Bierbrauer, J., Black, S. & Edel, Y. Some t-Homogeneous Sets of Permutations. Designs, Codes and Cryptography 9, 29–38 (1996). https://doi.org/10.1023/A:1027333822360
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DOI: https://doi.org/10.1023/A:1027333822360