We continue the work of the previous paper (Hachenberger, Finite Fields Appl., in press), and, generalizing some of the results obtained there, we give explicit constructions of free and completely free elements in GF(q r n ) over GF(q), where n is any nonnegative integer and where r is any odd prim
β¦ LIBER β¦
Completely Normal Elements in Iterated Quadratic Extensions of Finite Fields
β Scribed by Robin Chapman
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 226 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
β¦ Synopsis
Cohen and McNay both give iterative constructions of irreducible polynomials of 2-power degree over finite fields of odd order. In this paper I show that the roots of these polynomials are completely normal elements in the appropriate extension field.
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A characterization of normal bases and complete normal bases in GF(q r n ) over GF(q), where q ΟΎ 1 is any prime power, r is any prime number different from the characteristic of GF(q), and n Υ 1 is any integer, leads to a general construction scheme of series (v n ) nΥ0 in GF(q r Θ ) :Ο Κ nΥ0 GF(q r