Duality of codes and theta functions. (Q2740975)
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scientific article; zbMATH DE number 1642188
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Duality of codes and theta functions. |
scientific article; zbMATH DE number 1642188 |
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17 September 2002
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self-dual codes
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theta functions
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MacWilliams identity
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weight enumerator polynomials
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Duality of codes and theta functions. (English)
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The author establishes a connection between weight enumerator polynomials of codes and modular forms based on the observation that the MacWilliams identity for the doubly-even self-dual code \(C\) is just the inversion formula of the theta function of the associated even unimodular lattice \(\Gamma_C\). Those not familiar with the subject can find a detailed introduction in, for example, Chapter 3 of [\textit{W. Ebeling}, Lattices and codes, 2nd ed. (Vieweg; Wiesbaden) (2002; Zbl 1030.11030)].
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