## 59 Citations

Even unimodular Euclidean lattices of dimension 32.II

- Mathematics
- 1984

The problem of generating 32-dimensional even unimodular Euclidean lattices by vectors of a given length is studied fully. It is proved that, apart from 15 exceptions, such lattices are generated by…

Low-dimensional lattices. I. Quadratic forms of small determinant

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1988

In this paper, the first of a series dealing with low-dimensional lattices and their applications, we classify positive-definite integral quadratic forms of determinant d ≼ 25 in dimensions up to a…

Even positive definite unimodular quadratic forms over (√3)

- Mathematics
- 1991

A complete list of even unimodular lattices over Q(\/3) is given for each dimension n = 2, 4, 6, 8 . Siegel's mass formula is used to verify the completeness of the list. Alternate checks are given…

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

- MathematicsEur. J. Comb.
- 1982

Self-Dual Codes over Z 4 and Unimodular Lattices : A Survey

- Mathematics, Computer Science
- 2002

In this survey, basic facts of life in the Z4 world, known families of are reviewed, and the Leech lattice is reviewed.

Low-dimensional lattices. IV. The mass formula

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1988

The mass formula expresses the sum of the reciprocals of the group orders of the lattices in a genus in terms of the properties of any of them. We restate the formula so as to make it easier to…

The Covering Radius of the Leech Lattice

- Physics
- 1993

We investigate the points in 24-dimensional space that are at maximal distance from the Leech lattice, i.e. the “deep holes” in that lattice.

The Reflective Lorentzian Lattices of Rank 3

- Mathematics
- 2010

The author classifies all the symmetric integer bilinear forms of signature $(2,1)$ whose isometry groups are generated up to finite index by reflections. There are 8,595 of them up to scale, whose…

## References

SHOWING 1-10 OF 18 REFERENCES

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

- MathematicsEur. J. Comb.
- 1982

Tables of sphere packings and spherical codes

- MathematicsIEEE Trans. Inf. Theory
- 1981

The theta functions of a number of important packings and tables of the first fifty or so of their coefficients are given in this paper.

A Course in Arithmetic

- Mathematics
- 1973

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…

Relations between combinatorics and other parts of mathematics

- Mathematics
- 1979

Brings into focus interconnections between combinatorics on the one hand and geometry, group theory, number theory, special functions, lattice packings, logic, topological embeddings, games,…

Extremal self-dual lattices exist only in dimensions 1 to 8

- Mathematics
- 1978

It is known that if A is a self-dual lattice in R", then min {u-u | u e A, u # 0} < (M/8) + 1. If equality holds the lattice is called extremal. In this paper we find all the extremal lattices: there…

Self-dual codes over GF(3) and GF(4) of length not exceeding 16

- Computer ScienceIEEE Trans. Inf. Theory
- 1979

All self-dual codes over GF(3) and GF(4) of length 16 are found and several new extremal self- dual codes are given which have length greater than 16.

Introduction to quadratic forms

- Mathematics
- 1963

Prerequisites ad Notation Part One: Arithmetic Theory of Fields I Valuated Fields Valuations Archimedean Valuations Non-Archimedean valuations Prolongation of a complete valuation to a finite…

Gesammelte Abhandlungen

- EconomicsNature
- 1906

THE first volume of Prof. Abbe's works has already been noticed in the pages of NATURE (vol. lxix., p. 497). The contents of the second volume, while extremely interesting, are more miscellaneous in…