Bulletin (New Series) of the American Mathematical Society

A new upper bound for the minimum of an integral lattice of determinant 1

J. H. Conway and N. J. A. Sloane

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Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 23, Number 2 (1990), 383-387.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183555887

Mathematical Reviews number (MathSciNet)
MR1046123

Zentralblatt MATH identifier
0709.11030

Subjects
Primary: 11E25: Sums of squares and representations by other particular quadratic forms 11E41: Class numbers of quadratic and Hermitian forms 11H31: Lattice packing and covering [See also 05B40, 52C15, 52C17] 52A45 94B05: Linear codes, general

Citation

Conway, J. H.; Sloane, N. J. A. A new upper bound for the minimum of an integral lattice of determinant 1. Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 383--387. https://projecteuclid.org/euclid.bams/1183555887


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References

  • 1. R. E. Borcherds, The Leech lattice and other lattices, Ph.D. dissertation, Univ. of Cambridge, 1984.
  • 2. J. H. Conway, A. M. Odlyzko, and N. J. A. Sloane, Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23 and 24, Mathematika 25 (1978), 36-43.
  • 3. J. H. Conway and V. Pless, On the enumeration of self-dual codes, J. Combin. Theory Ser. A 28 (1980), 26-53.
  • 4. J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Springer-Verlag, New York, 1988.
  • 5. G. A. Kabatiansky and V. I. Levenshtein, Bounds for packings on a sphere and in space, (in Russian), Problemy Peredachi Informatsii 14 (1) (1978), 3-25.
  • 6. F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, North-Holland, Amsterdam, 1977.
  • 7. C. L. Mallows, A. M. Odlyzko, and N. J. A. Sloane, Upper bounds for modular forms, lattices, and codes, J. Algebra 36 (1975), 68-76.
  • 8. C. L. Mallows and N. J. A. Sloane, An upper bound for self-dual codes, Inform, and Control 22 (1973), 188-200.
  • 9. R. J. McEliece, E. R. Rodemich, H. C. Rumsey, Jr., and L. R. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans. Inform. Theory 23 (1977), 157-166.
  • 10. J. Milnor and D. Husemoller, Symmetric bilinear forms, Springer-Verlag, New York, 1973.
  • 11. C. L. Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Göttingen Nach. 10 (1969), 87-102. (Gesam. Abh. vol. IV, pp. 82-97.)
  • 12. E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge Univ. Press, 1963.

See also

  • Errata: Erratum. Bull. Amer. Math. Soc. (N.S.), Volume 24, Number 2 (1991), 479--479.