An improvement on the bounds of Weil exponential sums over Gallois rings with some applications

Date

2004-10-01

Author

Ling, S
Özbudak, Ferruh

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We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum distance of certain trace codes over Z(p)2 and the bounds on the correlation of certain nonlinear p-ary sequences.

Subject Keywords

Library and Information Sciences, Information Systems, Computer Science Applications

URI

https://hdl.handle.net/11511/34608

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

DOI

https://doi.org/10.1109/tit.2004.834743

Collections

Department of Mathematics, Article

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Citation Formats

S. Ling and F. Özbudak, “An improvement on the bounds of Weil exponential sums over Gallois rings with some applications,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 2529–2539, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34608.