Titlebook: Sphere Packings, Lattices and Groups; J. H. Conway,N. J. A. Sloane Book 19932nd edition Springer Science+Business Media New York 1993 Dime

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J. H. Conway,A. M. Odlyzko,N. J. A. Sloaneird edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in:.the existence and uniqueness of solutions;.impact

悠然

Subjugate

Further Connections Between Codes and Lattices,This chapter contains further investigations of the connections between codes and sphere packings. Constructions A and B of Chapter 5 are analyzed in greater detail and are generalized to complex lattices. We also study self-dual codes and lattices and their weight enumerators and theta series.

ferment

A Characterization of the Leech Lattice,We give a short proof that Leech’s remarkable lattice is characterized by some of its simplest properties.

Budget

Bounds on Kissing Numbers,Upper bounds are given on the maximal number, τ., of nonoverlapping unit spheres that can touch a unit sphere in .-dimensional Euclidean space, for . ⩽ 24. In particular it is shown that τ. = 240 and τ. = 196560.

巨硕

Enumeration of Unimodular Lattices,In this chapter we state explicit formulae for the Minkowski-Siegel mass constants for unimodular lattices. We give Niemeier’s list of 24-dimensional even unimodular lattices, use the mass constant to verify that it is correct, and then enumerate all unimodular lattices of dimension . ⩽ 23.

熄灭

The 24-Dimensional Odd Unimodular Lattices,This chapter completes the classification of the 24-dimensional unimodular lattices by enumerating the odd lattices. These are in one-to-one correspondence with neighboring pairs of Niemeier lattices.

violate

Even Unimodular 24-Dimensional Lattices,Niemeier’s classification of even unimodular 24-dimensional lattices is simplified. The methods involve the theory of modular forms, algebraic coding, and root systems.

骇人

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