Titlebook: Lattices and Codes; A Course Partially B Wolfgang Ebeling Textbook 19941st edition Springer Fachmedien Wiesbaden 1994 Dimension.algebra.cla

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https://doi.org/10.1007/978-3-322-96879-1Dimension; algebra; classification; code; coding; coding theory; design; error-correcting code; history; info

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Lattices and Codes,In this section we introduce the basic concept of a lattice in ?.. For references see [Ser73], [MH73], [Cas78], [Kne74], and [O’M63].

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Theta Functions and Weight Enumerators,Let Г ? ?. be a lattice. We associate toTa function which is defined on the upper half plane

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Even Unimodular Lattices,In this section we study modified theta functions, namely theta series with spherical coefficients, and their behavior under transformations of the modular group. The results of this section are due to E. Hecke [Hec40] and B. Schoeneberg [Sch39, Sch74]. Our presentation follows [Ogg69, Chap. VI] and [Sko87].

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The Leech Lattice,In §2.8 we defined an even unimodular lattice A. ? ?. with . ≥ 4 for all . ∈ A.: the Leech lattice. This chapter is devoted to this important lattice. We shall first show the uniqueness of this lattice. We shall prove the following theorem.

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Springer Fachmedien Wiesbaden 1994

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Lattices and Codes978-3-322-96879-1Series ISSN 0932-7134 Series E-ISSN 2512-7039

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