Etude algorithmique de réseaux construits avec la forme trace. (Algorithmic study of lattices constructed by means of the trace form). (French) Zbl 0787.11024

The authors study the numerical properties of three types of lattices constructed by means of the trace form in cyclotomic number fields and: calculate their minimum and minimal vectors; determine whether or not they are perfect or eutactic. The lattices considered are: certain even unimodular lattices, constructed by E. Bayer-Fluckiger [Comment. Math. Helv. 59, 509-538 (1984; Zbl 0558.10029)], of minimum 4 and dimension 24 (Leech lattice [J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups (1988; Zbl 0634.52002), (2nd ed. 1993; Zbl 0785.11036)]), 32 and 48; certain lattices related to the Leech lattice; and Craig’s lattices (ibid.), constructed using the successive powers of the ideal above \(p\) in the \(p\)-th cyclotomic field.
Reviewer: E.L.Cohen (Ottawa)


11H31 Lattice packing and covering (number-theoretic aspects)
11R18 Cyclotomic extensions
11Y99 Computational number theory


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