Abstract/Details

## On some general polynomials over finite fields

Sun, Jung-Fang.
University of South Florida ProQuest Dissertations Publishing,  1991. 9135823.

### Abstract (summary)

The theory of polynomials over finite fields plays an important role in studying the algebraic structure of finite fields. Especially, the study of reducibility or irreducibility of polynomials becomes an essential task when one studies the theory of finite fields and its applications.

Much research has been done on trinomials over a finite field, because of their relationship to the famous discrete log problem. This paper considers polynomials of more general type which have some of the trinomials as special cases.

The first family of polynomials to be considered are of the form $f(x) = x\sp{q\sp3+q\sp2+q+1}{-}ax\sp{q\sp2+q+1}{-}bx\sp{q+1}{-}cx{-}d,$ with $q=p\sp r$ over $F\sb{p\sp s}$, which is an extension of results by Agou (12). The result is then extended to the study of polynomials of the form $f(x)$ = $x\sp{q\sp4+q\sp3+q\sp2+q+1}{-}ax\sp{q\sp3+q\sp 2+q+1}{-}bx\sp{q\sp2+q+1}{-}cx\sp{q+1}{-}dx{-}e,$ with $q=p\sp r$ over $F\sb{p\sp s}$. Furthermore, the general form of the above polynomials, $f(x)$ = $x\sp{q\sp n+\cdots +1}{-}a\sb1x\sp{q\sp{n-1}+\cdots +1}{-}a\sb{n}x{-}a\sb{n+1},$ with $q=p\sp r$ over $F\sb{p\sp s}$ will be discussed.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
On some general polynomials over finite fields
Author
Sun, Jung-Fang
Number of pages
110
Degree date
1991
School code
0206
Source
DAI-B 52/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-208-06503-7
Liang, Joseph J.
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9135823
ProQuest document ID
303936315