The extension theorem for the Lee and Euclidean weights over \(\mathbb{Z}/p^k \mathbb{Z}\) (Q1621576)
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scientific article; zbMATH DE number 6975782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The extension theorem for the Lee and Euclidean weights over \(\mathbb{Z}/p^k \mathbb{Z}\) |
scientific article; zbMATH DE number 6975782 |
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The extension theorem for the Lee and Euclidean weights over \(\mathbb{Z}/p^k \mathbb{Z}\) (English)
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9 November 2018
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The authors show that the Lee and Euclidean weights have the extension property over \(\mathbb{Z}/p^k\mathbb{Z}\), that is that any isometry of the code with respect to the Lee or Euclidean weight extends to an isometry of the ambient space. The technique of proof involves expressing certain Fourier coefficients in terms of Bernoulli numbers and knowing the locations of zeros of Dirichlet \(L\)-functions.
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extension theorem
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Lee weight
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Euclidean weight
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