Constructing integral lattices with prescribed minimum. I
HTML articles powered by AMS MathViewer
- by W. Plesken and M. Pohst PDF
- Math. Comp. 45 (1985), 209-221 Request permission
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.References
- John Cannon, A general purpose group theory program, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Lecture Notes in Math., Vol. 372, Springer, Berlin, 1974, pp. 204–217. MR 0354823
- J. H. Conway and N. J. A. Sloane, Laminated lattices, Ann. of Math. (2) 116 (1982), no. 3, 593–620. MR 678483, DOI 10.2307/2007025
- J. H. Conway and N. J. A. Sloane, Complex and integral laminated lattices, Trans. Amer. Math. Soc. 280 (1983), no. 2, 463–490. MR 716832, DOI 10.1090/S0002-9947-1983-0716832-0
- John Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745. MR 285994, DOI 10.4153/CJM-1971-081-3
- Jeffrey S. Leon, Computing automorphism groups of combinatorial objects, Computational group theory (Durham, 1982) Academic Press, London, 1984, pp. 321–335. MR 760667
- John Milnor and Dale Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73, Springer-Verlag, New York-Heidelberg, 1973. MR 0506372 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. H. Robertz, Eine Methode zur Berechnung der Automorphismengruppe einer endlichen Gruppe, Diplomarbeit, Aachen, 1976.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Math. Comp. 45 (1985), 209-221
- MSC: Primary 11H31; Secondary 11H50
- DOI: https://doi.org/10.1090/S0025-5718-1985-0790654-2
- MathSciNet review: 790654