Name
Abstract | ||
|---|---|---|
Normal bases in finite fields constitute a vast topic of large theoretical and practical interest. Recently, $k$-normal elements were introduced as a natural extension of normal elements. The existence and the number of k-normal elements in a fixed extension of a finite field are both open problems in full generality, and comprise a promising research avenue. In this paper, we first formulate a general lower bound for the number of k-normal elements, assuming that they exist. We further derive a new existence condition for k-normal elements using the general factorization of the polynomial $x^m - 1$ into cyclotomic polynomials. Finally, we provide an existence condition for normal elements in $F_{q^m}$ with a non-maximal but high multiplicative order in the group of units of the finite field. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/978-3-030-68869-1_15 | WAIFI |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simran Tinani | 1 | 0 | 0.34 |
| Joachim Rosenthal | 2 | 0 | 0.34 |