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Large Set Complete Mappings Over Fin...

Hearding, Paul,

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Large Set Complete Mappings Over Finite Fields /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Large Set Complete Mappings Over Finite Fields // Paul Hearding.
Author:	Hearding, Paul,
Description:	1 electronic resource (88 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
Contained By:	Dissertations Abstracts International86-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31839445
ISBN:	9798315701637

Large Set Complete Mappings Over Finite Fields /
Hearding, Paul,

Large Set Complete Mappings Over Finite Fields /Paul Hearding. - 1 electronic resource (88 pages)

Source: Dissertations Abstracts International, Volume: 86-11, Section: B.

This thesis explores set complete mappings and permutation polynomials of a newly defined type. We begin with some preliminaries in Chapter 1 to build up the tools and vocabulary necessary for such an exploration. Then, in Chapter 2, we introduce a new methodology for establishing permutation polynomials from Dembowski-Ostrom polynomials over Fq. In Chapters 3 and 4, we present new classes of permutation polynomials and set complete mappings. In Chapter 5, we survey what is known of monomial set complete mappings and present some computational data. Finally, in Chapter 6, we share a couple of conjectures and plot the course for future work.

English

ISBN: 9798315701637Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Finite fields

Large Set Complete Mappings Over Finite Fields /
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020 $a 9798315701637
035 $a (MiAaPQD)AAI31839445
035 $a AAI31839445
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Hearding, Paul, $e author. $3 3822961
245 1 0 $a Large Set Complete Mappings Over Finite Fields / $c Paul Hearding.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (88 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
500 $a Advisors: Coulter, Robert Committee members: Cioaba, Sebastian; Senger, Steven; Li, Shuxing.
502 $b Ph.D. $c University of Delaware $d 2025.
520 $a This thesis explores set complete mappings and permutation polynomials of a newly defined type. We begin with some preliminaries in Chapter 1 to build up the tools and vocabulary necessary for such an exploration. Then, in Chapter 2, we introduce a new methodology for establishing permutation polynomials from Dembowski-Ostrom polynomials over Fq. In Chapters 3 and 4, we present new classes of permutation polynomials and set complete mappings. In Chapter 5, we survey what is known of monomial set complete mappings and present some computational data. Finally, in Chapter 6, we share a couple of conjectures and plot the course for future work.
546 $a English
590 $a School code: 0060
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Computational physics. $3 3343998
653 $a Finite fields
653 $a Permutation polynomials
653 $a Set complete mappings
653 $a Computational data
690 $a 0405
690 $a 0216
690 $a 0364
710 2 $a University of Delaware. $b Mathematical Sciences. $e degree granting institution. $3 3822962
720 1 $a Coulter, Robert $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-11B.
790 $a 0060
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31839445