有限域上的正規(guī)基、最優(yōu)正規(guī)基和對偶基.pdf

1、四川大學(xué)博士學(xué)位論文作者鏖壁甚完成日期2QQ量年』衛(wèi)月上業(yè)日培養(yǎng)單位望刖盤鱟熬堂堂瞳指導(dǎo)教師型：魚墊筮專授予學(xué)位日期四jll大學(xué)博士學(xué)位論文AbstractNormalBases，OptimalNormalBasesandTheirDualBasesOverFiniteFieldsMajor：AppliedNumberTheoryAuthor：LIAOQunyingSupervisor：SUNQiThispaperconsistsoft

2、hreechaptersInchapter1，wehavegiventwoveryusefulalgorithmstOcomputemultiplicationtablesofoptimalnormalbasesoverfinitefieldsThroughcomparingthesealgorithmswithotherwellknowntwoalgorithmswefoundthattheseagorithmsareverybeau

3、tifulInchapter2wehavediscussedtherelationshipofnormalbasesandtheirdualnormalbasesoverfinitefieldsWenotonlygotsomesufficientandnecessaryCOn—ditionsforwhichanormalbasisoranoptimalnormalbasisiSequivalenttoitSdualnormalbasis

4、overfinitefields，andobtmnedallselfdualoptimalnormalbasesoverfi—nitefields，butalsodiscussedothertwoextensionsofselfdualnormalbaseswhicharcweaklynormalbasesandthenormalbasiswhosedualbasisisgeneratedbyitsgen—erator’Slinearl

5、ycombinations，andobtainedsomepropertiesfortheirmultiplicationtablesandcomplexitiesInchapter3，weprovedthatthedistributionofprimitiveelementsofF=RninⅣ哥島(∥)isuniformly，whereⅣ爿島(盧)=Q∈F：坼／‘(a)=序istheinversefunctionoftheNOrmfu

6、nctionNFRIQlofaoverFqWealsoobtainedseveralsufficientandnecessaryconditionsforprimitiveelementsandstudiedsomeparticularcasesforoptimalnormalbaseswhosegeneratorisaprimitiveelementofFKeyWords：Finitefields，Primitiveelements，