17
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

Classification of Two Genera of 32-Dimensional Lattices of Rank 8 over the Hurwitz Order

&
Pages 151-162 | Published online: 03 Apr 2012

REFERENCES

  • Bacher , R. and Venkov , B. B. 1996 . “Réseaux entiers unimodulaires sans racine en dimension 27 et 28” Grenoble : Institut Fourier. . [Bacher and Venkov 1996], preprint
  • Bachoc , C. 1995 . “Voisinage au sens de Kneser pour les réseaux quaternioniens” . Comment. Math. Helv. , 70 ( 3 ) : 350 – 374 . [Bachoc 1995]
  • Cohen , A. M. 1980 . “Finite quaternionic reflection groups” . J. Algebra , 64 ( 2 ) : 293 – 324 . [Cohen 1980]
  • Feit , W. 1978 . “Some lattices over Q(√–3)” . J. Algebra , 52 ( 1 ) : 248 – 263 . [Feit 1978]
  • Hashimoto , K.-i. 1980 . “On Brandt matrices associated with the positive definite quaternion Hermitian forms” . J. Fac. Sci. Univ. Tokyo Sect. I A Math. , 27 ( 1 ) : 227 – 245 . [Hashimoto 1980]
  • Kneser , M. 1957 . “Klassenzahlen deflniter quadratischer Formen” . Arch. Math. , 8 : 241 – 250 . [Kneser 1957]
  • Koch , H. and Nebe , G. 1993 . “Extremal even unimodular lattices of rank 32 and related codes” . Math. Nachr. , 161 : 309 – 319 . [Koch and Nebe 1993]
  • Koch , H. and Venkov , B. B. 1989 . “Über ganzzahlige unimodulare euklidische Gitter” . J. Reine Angew. Math. , 398 : 144 – 168 . [Koch and Venkov 1989]
  • Koch , H. and Venkov , B. B. 1991 . “Über gerade unimodulare Gitter der Dimension 32, III” . Math. Nachr. , 152 : 191 – 213 . [Koch and Venkov 1991]
  • MacWilliams , F. J. , Odlyzko , A. M. , Sloane , N. J. A. and Ward , H. N. 1978 . “Self-dual codes over GF(4)” . J. Combin. Theory Ser. A , 25 ( 3 ) : 288 – 318 . [MacWilliams et al. 1978]
  • Martinet , J. 1996 . Les réseaux parfaits des espaces euclidiens Masson, Paris : Mathématiques. . [Martinet 1996]
  • Nebe , G. 1990 . Wiedererkennung von Gittern Aachen : Diplomarbeit, Lehrstuhl B für Mathematik, RWTH. . [Nebe 1990]
  • Nebe , G. 1996 . “Finite subgroups of GLn(Q) for 25 ≤ n≤ 31” . Comm. Algebra , 24 ( 7 ) : 2341 – 2397 . [Nebe 1996]
  • Nebe , G. “Finite quaternionic matrix groups” [Nebe ≥ 1997], See http://samuel.math.rwth-aachen.de/~LBFM/gabi.Submitted
  • Nebe , G. and Plesken , W. 1995 . “Finite rational matrix groups” . Mem. Amer. Math. Soc. , 116 ( 556 ) : viii+144 [Nebe and Plesken 1995]
  • Plesken , W. and Souvignier , B. “Computing isometries of lattices” [Plesken and Souvignier ≥ 1997], To appear in J. Symbolic Comput.
  • Quebbemann , H.-G. 1984 . “An application of Siegel's formula over quaternion orders” . Mathematika , 31 ( 1 ) : 12 – 16 . [Quebbemann 1984]
  • Quebbemann , H.-G. 1995 . “Modular lattices in Euclidean spaces” . J. Number Theory , 54 ( 2 ) : 190 – 202 . [Quebbemann 1995]
  • Taylor , D. E. 1992 . The geometry of the classical groups Berlin : Heldermann Verlag. . [Taylor 1992], Sigma Series in Pure Mathematics
  • Tits , J. 1980 . “Four presentations of Leech's lattice”. ” . In Finite simple groups, II Edited by: Collins , M. J. 303 – 307 . London and New York : Academic Press. . [Tits 1980], (Durham, 1978)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.