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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Ebeling, Wolfgang. Lattices and codes. Braunschweig/Wiesbaden : Vieweg, ©1994 (DLC) 94193344 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Wolfgang Ebeling; Friedrich Hirzebruch |

ISBN: | 9783322968791 3322968790 |

OCLC Number: | 828774955 |

Language Note: | English. |

Description: | 1 online resource (xii, 178 pages) : illustrations. |

Contents: | 1 Lattices and Codes -- 1.1 Lattices -- 1.2 Codes -- 1.3 From Codes to Lattices -- 1.4 Root Lattices -- 1.5 Highest Root and Weyl Vector -- 2 Theta Functions and Weight Enumerators -- 2.1 The Theta Function of a Lattice -- 2.2 Modular Forms -- 2.3 The Poisson Summation Formula -- 2.4 Theta Functions as Modular Forms -- 2.5 The Eisenstein Series -- 2.6 The Algebra of Modular Forms -- 2.7 The Weight Enumerator of a Code -- 2.8 The Golay Code and the Leech Lattice -- 2.9 The MacWilliams Identity and Gleason’s Theorem -- 2.10 Quadratic Residue Codes -- 3 Even Unimodular Lattices -- 3.1 Theta Functions with Spherical Coefficients -- 3.2 Root Systems in Even Unimodular Lattices -- 3.3 Overlattices and Codes -- 3.4 The Classification of Even Unimodular Lattices of Dimension 24 -- 4 The Leech Lattice -- 4.1 The Uniqueness of the Leech Lattice -- 4.2 The Sphere Covering Determined by the Leech Lattice -- 4.3 Twenty-Three Constructions of the Leech Lattice -- 4.4 Embedding the Leech Lattice in a Hyperbolic Lattice -- 5 Lattices over Integers of Number Fields and Self-Dual Codes -- 5.1 Lattices over Integers of Cyclotomic Fields -- 5.2 Construction of Lattices from Codes over . |

Series Title: | Advanced lectures in mathematics. |

Responsibility: | Wolfgang Ebeling. |

### Abstract:

This volume is about the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings.
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