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

DOI10.1080/10586458.1997.10504603zbMath0886.11021OpenAlexW2077832222MaRDI QIDQ4369745

Christine Bachoc, Gabriele Nebe

Publication date: 23 April 1998

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1047650001

zbMATH Keywords

bipartite graphsHurwitz ordermass formulasgenus of hermitian unimodular lattices of rank eightKneser's neighboring method

Mathematics Subject Classification ID

Quadratic forms over global rings and fields (11E12) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items (10)

ON THE CLASSIFICATION OF EVEN UNIMODULAR LATTICES WITH A COMPLEX STRUCTURE ⋮ On the classification of lattices over \(\mathbb Q(\sqrt{-3})\), which are even unimodular \(\mathbb Z\)-lattices ⋮ Automorphisms of extremal unimodular lattices in dimension 72 ⋮ Simultaneous computation of Hecke operators ⋮ On the classification of lattices over \(\mathbb Q(\sqrt{-3})\) which are even unimodular \(\mathbb Z\)-lattices of rank 32 ⋮ Automorphic Forms on Feit’s Hermitian Lattices ⋮ New complex- and quaternion-hyperbolic reflection groups ⋮ Finite quaternionic matrix groups ⋮ The graded ring of quaternionic modular forms of degree 2 ⋮ Zonal functions for the unitary groups and applications to Hermitian lattices.

Cites Work

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• Klassenzahlen definiter quadratischer Formen
• Finite quaternionic reflection groups
• Some lattices over \(Q(\sqrt{-3})^*\)
• Self-dual codes over GF(4)
• Computing isometries of lattices
• Modular lattices in Euclidean spaces
• Neighborhood in the sense of Kneser for quaternionic lattices
• An application of Siegel's formula over quaternion orders
• Über gerade unimodulare Gitter der Dimension 32, III
• Finite quaternionic matrix groups
• Extremal Even Unimodular Lattices of Rank 32 and Related Codes
• Finite subgroups of GL_n(Q) for 25 ≤ n ≤ 31

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