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Local and Global Character Sums

✍ Scribed by Chunlei Liu

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2000
Tongue
English
Weight
122 KB
Volume
16
Category
Article
ISSN
1439-7617

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πŸ“œ SIMILAR VOLUMES

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

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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