Elements of prescribed order, prescribed traces and systems of rational functions over finite fields

Date

2005-01-01

Author

Özbudak, Ferruh

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Let k greater than or equal to 1 and f(1),..., f(r) is an element of F-qk (x) be a system of rational functions forming a strongly linearly independent set over a finite field F-q. Let gamma(1),..., gamma(r) is an element of F-q be arbitrarily prescribed elements. We prove that for all sufficiently large extensions F-qkm, there is an element xi is an element of F-qkm of prescribed order such that Tr-Fqkm /Fq (f(i) (xi)) = gamma(i) for i = 1,..., r, where Tr-Fqkm/fq is the relative trace map from F-qkm onto F-q. We give some applications to BCH codes, finite field arithmetic and ordered orthogonal arrays. We also solve a question of Helleseth et al. (Hypercubic 4 and 5-designs from Double-Error-Correcting codes, Des. Codes. Cryptgr. 28(2003). pp. 265-282) completely.

Subject Keywords

Applied Mathematics, Computer Science Applications

URI

https://hdl.handle.net/11511/40865

Journal

DESIGNS CODES AND CRYPTOGRAPHY

DOI

https://doi.org/10.1007/s10623-003-4193-0

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak, “Elements of prescribed order, prescribed traces and systems of rational functions over finite fields,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 35–54, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40865.