Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by nonprincipal ideals yields simple constructions of further lattices including the Leech lattice.

We shall consider higher power residue codes over the ring Z4. We will briefly introduce these codes over Z4 and then we will find a new construction for the Leech lattice. A similar construction is… Expand

Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on… Expand

Certain self-dual codes over Z/sub 4/ are shown to determine even unimodular lattices, including the extended quadratic residue code of length q+1, where q/spl equiv/-1(mod8) is a prime power.Expand

Proceedings of IEEE International Symposium on Information Theory

1997

Bonnecaze, Calderbank and Sole (see IEEE Trans. Inform. Theory, vol.41, p.366-77, 1995) introduced for primes p/spl equiv//spl plusmn/(mod8), codes /spl Qscr/ and /spl Nscr/, the universal extended… Expand

These notes are to supplement my paper (4), and should be read in conjunction with it. Both are divided into three parts, and in these notes the section numbers have a further digit added; thus §1.41… Expand