Conference Matrices and Unimodular Lattices

  title={Conference Matrices and Unimodular Lattices},
  author={Robin J. Chapman},
  journal={Eur. J. Comb.},
  • R. Chapman
  • Published 19 July 2000
  • Computer Science, Mathematics
  • Eur. J. Comb.
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. 
Steinitz classes of unimodular lattices
  • R. Chapman
  • Computer Science, Mathematics
    Eur. J. Comb.
  • 2004
Higher Power Residue Codes and 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
On the classification of self-dual [20, 10, 9] codes over GF(7)


A Course in Arithmetic
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
Quaternary quadratic residue codes and unimodular lattices
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.
Universal codes and unimodular lattices
  • R. Chapman, P. Solé
  • Mathematics
    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
Notes on sphere packings
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
  • Solé & A. R. Calderbank, ‘Quaternary quadratic residue codes and unimodular lattices’ IEEE Trans. Inform. Theory 41
  • 1995
Algebra vol
  • 2 (2nd ed.), John Wiley & Sons
  • 1989
Notes on sphere packing
  • Canad. J. Math
  • 1967