The Unimodular Lattices of Dimension up to 23 and the Minkowski-Siegel Mass Constants

In an earlier paper we enumerated the integral lattices of determinant one and dimension not exceeding 20. The present paper extends this enumeration to dimension 23, finding 40 lattices of dimension 21, 68 of dimension 22, and 117 of dimension 23. We also give explicit formulae for the Minkowski-Siegel mass constants for unimodular lattices (apparently not stated correctly elsewhere in the literature) and an exact table of the mass constants up to 32 dimensions, which provided a valuable check on our enumeration

Gitter und Anwendungen

The meeting focussed on lattices and their applications in mathematics and information technology. The research interests of the participants varied from engineering sciences, algebraic and analytic number theory, coding theory, algebraic geometry to name only a few