Abstract

In Chapter IV, we have proved the existence of completely free elements in finite fields. As an essential tool, we have used the Reduction Theorem (Section 4). However, as already mentioned in Section 6, the Reduction Theorem does not give a characterization of completely free elements. As a further example, let us once more consider the 21-dimensional extension over GF(2): The number of (completely) free elements in GF(23) over GF(2) by Theorem 10.5 is equal to 3; the number of (completely) free elements in GF(27) over GF(2) is equal to 49. Thus, the Reduction Theorem shows that there are at least 147 completely free elements in GF(221) over GF(2). However, in Example 14.6 (together with results from Section 15) we have seen that the exact number of completely free elements in that extension is equal to 259 308.

Full Text

Published Version

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.