Lattices and association schemes : a unimodular example without roots in dimension 28

Roland Bacher; Boris Venkov

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 5, page 1163-1176
  • ISSN: 0373-0956

Abstract

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Some interesting lattices can be constructed using association schemes. We illustrate this by a unimodular lattice without roots of dimension 28 which admits Sp ( 6 , 𝔽 3 ) · 2 as its automorphism group.

How to cite

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Bacher, Roland, and Venkov, Boris. "Lattices and association schemes : a unimodular example without roots in dimension 28." Annales de l'institut Fourier 45.5 (1995): 1163-1176. <http://eudml.org/doc/75154>.

@article{Bacher1995,
abstract = {Some interesting lattices can be constructed using association schemes. We illustrate this by a unimodular lattice without roots of dimension 28 which admits $\{\rm Sp\}(6,\{\Bbb F\}_3)\cdot 2$ as its automorphism group.},
author = {Bacher, Roland, Venkov, Boris},
journal = {Annales de l'institut Fourier},
keywords = {lattice; association scheme; symplectic space; spread},
language = {eng},
number = {5},
pages = {1163-1176},
publisher = {Association des Annales de l'Institut Fourier},
title = {Lattices and association schemes : a unimodular example without roots in dimension 28},
url = {http://eudml.org/doc/75154},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Bacher, Roland
AU - Venkov, Boris
TI - Lattices and association schemes : a unimodular example without roots in dimension 28
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 5
SP - 1163
EP - 1176
AB - Some interesting lattices can be constructed using association schemes. We illustrate this by a unimodular lattice without roots of dimension 28 which admits ${\rm Sp}(6,{\Bbb F}_3)\cdot 2$ as its automorphism group.
LA - eng
KW - lattice; association scheme; symplectic space; spread
UR - http://eudml.org/doc/75154
ER -

References

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  10. [Gr] B.H. GROSS, Group representations and lattices, J. Amer. Math. Soc., 3 (1990), 929-960. Zbl0745.11035MR92a:11077
  11. [ST] R. SCHARLAU, P.H. TIEP, Symplectic groups, symplectic spreads, codes and unimodular lattices, preprint. Zbl0887.20004
  12. [Th] J.G. THOMPSON, Finite groups and even lattices, J. Algebra, 38 (1976), 523-524. Zbl0344.20001MR53 #3108
  13. [Wa1] H.N. WARD, Representations of symplectic Groups, J. Algebra, 20 (1972), 182-195. Zbl0239.20013MR44 #4116
  14. [Wa2] H.N. WARD, Quadratic Residue Codes and Symplectic Groups, J. Algebra, 29 (1974), 150-171. Zbl0276.94002MR56 #2648

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