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

被引:2
作者
Özbudak, F [1 ]
机构
[1] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey
关键词
finite field; algebraic function field; BCH code; ordered orthogonal array;
D O I
10.1007/s10623-003-4193-0
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
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.
引用
收藏
页码:35 / 54
页数:20
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