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Constructing integral lattices with prescribed minimum. I

Authors: W. Plesken and M. Pohst
Journal: Math. Comp. 45 (1985), 209-221, S5
MSC: Primary 11H31; Secondary 11H50
MathSciNet review: 790654
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Abstract: Methods for computing integral laminated lattices with prescribed minimum are developed. Laminating is a process of stacking layers of an $ (n - 1)$-dimensional lattice as densely as possible to obtain an n-dimensional lattice. Our side conditions are: All scalar products of lattice vectors are rational integers, and all lattices are generated by vectors of prescribed minimum (square) length m. For $ m = 3$ all such lattices are determined.

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  • [1] J. Cannon, A General Purpose Group Theory Program, Proc. Second Internat. Conf. Theory of Groups, Canberra 1973, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin and New York, 1974, pp. 204-217. MR 0354823 (50:7300)
  • [2] J. H. Conway & N. J. A. Sloane, "Laminated lattices," Ann. of Math., v. 116, 1982, pp. 593-620. MR 678483 (84c:52015)
  • [3] J. H. Conway & N. J. A. Sloane, "Complex and integral laminated lattices," Trans. Amer. Math. Soc., v. 280, 1983, pp. 463-490. MR 716832 (86e:11052)
  • [4] J. Leech & N. J. A. Sloane, "Sphere packings and error-correcting codes," Canad. J. Math., v. 23, 1971, pp. 718-745. MR 0285994 (44:3211)
  • [5] J. S. Leon, "Computing automorphism groups of combinatorial objects," in Computational Group Theory (M. D. Atkinson, ed.), Academic Press, London, New York, 1984, pp. 321-336. MR 760667 (86j:05004)
  • [6] J. Milnor & D. Husemoller, Symmetric Bilinear Forms, Ergebnisse Math. Grenzgeb., Band 73, Springer-Verlag, Berlin and New York, 1973. MR 0506372 (58:22129)
  • [7] M. Pohst, "On the computation of lattice vectors of minimal length, successive minima, and reduced bases with applications," ACM Sigsam Bull., v. 15, 1981, pp. 37-44.
  • [8] H. Robertz, Eine Methode zur Berechnung der Automorphismengruppe einer endlichen Gruppe, Diplomarbeit, Aachen, 1976.

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Article copyright: © Copyright 1985 American Mathematical Society

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