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Linear Codes and Character Sums

✍ Scribed by Nathan Linial*; Alex Samorodnitsky†

Publisher
Springer-Verlag
Year
2002
Tongue
English
Weight
344 KB
Volume
22
Category
Article
ISSN
0209-9683

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📜 SIMILAR VOLUMES

On character sums and codes
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Coding-theoretical methods are used to obtain improved lower bounds for character sums induced by a multiplicative character of an arbitrary order over GF(q).

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A cyclic arithmetic code is a subgroup of \(\mathbf{Z} /\left(r^{n}-1\right) \mathbf{Z}\), where the weight of a word \(x\) is the minimal number of nonzero coefficients in the representation \(x \equiv \sum_{i=0}^{n-1} c_{i} r^{i}\) with \(\left|c_{i}\right|<r\) for all \(i\). A code is called equi

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✍ Mehmet Cenkci; Mümün Can; Veli Kurt 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 173 KB

In this paper, we study on two subjects. We first construct degenerate analogues of Dedekind sums in the sense of Apostol, Carlitz and Takács, and prove the corresponding reciprocity formulas. Secondly, we define generalized Dedekind character sums, which are explicit extensions of Berndt's definiti