Lattices with theta functions for G(√2) and linear codes

AbstractModular hermitian lattices over Z[i]and, in particular, unimodular lattices over Z[eπi4] give rise to modular forms for Hecke's group G(2)=<(1201), (01−10)>.Two general constructions of such lattices are performed, using codes over F2 and F9. Lattices with an extremal theta-function (i.e., with the largest minimum that Hecke's theory allows) are obtained in C2n for all n < 12, including the densest known sphere-packings of R4n for n = 1, 4, and 8