Abstract
Results of F. Özbudak on the existence of elements in a finite extension of a finite field with specified order and at which given rational functions have specified traces over the ground field are obtained by the method of character sums. There are significant applications to the construction of ordered arrays.
Similar content being viewed by others
References
S. D. Cohen (1990) ArticleTitlePrimitive elements and polynomials with arbitrary trace Discrete Mathematics 83 1–7 Occurrence Handle10.1016/0012-365X(90)90215-4
S. D. Cohen (2000) ArticleTitleKloosterman sums and primitive elements in Galois fields Acta Arith. 94 173–201
S. D. Cohen (2003) ArticleTitleThe orders of related elements of a finite field Ramanujan Journal 7 169–183 Occurrence Handle10.1023/A:1026295128600
S. D. Cohen Wenpeng Zhang (2002) ArticleTitleSums of two exact powers Finite Fields and their Application 8 471–477
T. Helleseth T. Kløve V. I. Levenshtein (2003) ArticleTitleHypercubic 4 and 5-designs from double-error-correcting BCH codes Designs, Codes and Cryptography 28 265–282
W.-C. Winnie Li (1999) ArticleTitleCharacter sums over p-adic fields Journal of Number Theory 74 181–229 Occurrence Handle10.1006/jnth.1998.2328
D. J. Madden (1981) ArticleTitlePolynomials and primitive roots in finite fields Journal of Number Theory 13 499–514 Occurrence Handle10.1016/0022-314X(81)90041-X
C. J. Moreno O. Moreno (1991) ArticleTitleExponential sums and Goppa codes: I Proceedings of American Mathematical Society 111 523–531
F. Özbudak (2005) ArticleTitleElements of prescribed order, prescribed traces and systems of rational functions over finite fields Design Codes and Cryptography 34 35–54 Occurrence Handle10.1007/s10623-003-4193-0 Occurrence HandleMR2126576
G. I. Perel’muter (1963) ArticleTitleOn certain character sums Uspehi Matematisk Nauk 18 145–149
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS classification: 11T30, 11T24
Rights and permissions
About this article
Cite this article
Cohen, S.D. Finite Field Elements with Specified Order and Traces. Des Codes Crypt 36, 331–340 (2005). https://doi.org/10.1007/s10623-004-1724-2
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10623-004-1724-2