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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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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.