![](/images/graphics-bg.png)
On the Polynomial Basis of GF(2n) Having a Small Number of Trace-One Elements
Joint Authors
Wang, Jiantao
Zheng, Dong
Huang, Zheng
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-12-05
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
In the Galois fields GF(2n), a polynomial basis with a small number of trace-one elements is desirable for its convenience in computing.
To find new irreducible polynomials g(x) over GF(2) with this property, we research into the auxiliary polynomial f(x)=(x+1)g(x) with roots {1,α1,α2,…,αn}, such that the symmetric polynomials sk=1+α1k+α2k+⋯+αnk are relative to the symmetric polynomials of g(x).
We introduce a new class of polynomials with the number “1” occupying most of the values in its sk.
This indicates that the number “0” occupies most of the values of the traces of the elements {α1,α2,…,αn}.
This new class of polynomial gives us an indirect way to find irreducible polynomials having a small number of trace-one elements in their polynomial bases.
American Psychological Association (APA)
Wang, Jiantao& Zheng, Dong& Huang, Zheng. 2016. On the Polynomial Basis of GF(2n) Having a Small Number of Trace-One Elements. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1112813
Modern Language Association (MLA)
Wang, Jiantao…[et al.]. On the Polynomial Basis of GF(2n) Having a Small Number of Trace-One Elements. Mathematical Problems in Engineering No. 2016 (2016), pp.1-6.
https://search.emarefa.net/detail/BIM-1112813
American Medical Association (AMA)
Wang, Jiantao& Zheng, Dong& Huang, Zheng. On the Polynomial Basis of GF(2n) Having a Small Number of Trace-One Elements. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1112813
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112813