特征$ne 2$的有限域上对称矩阵

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2、daTik
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3、dhb
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4、lutionstotheSymmetricMatrixEquationoveraFiniteFieldofCh.
=2andRepresentationofItsq-hypergeometricSeriesWeiHongzengZhangYibin(HebeiNormalUniversity,Shijiazhuang050091,China)AbstractLetFqbeafinitefieldwithqelements,whereqisapowerofanoddprime.Inthispaper,usingsingularorthogonalgoemetryoverFq,we

5、havegiventhenumberofsolutionsXofrankkandsolutionsXtotheequationXAX
=BoverF,qwhenAandBaresymmetricmatricesofordern,rank2ν+δandorderm,rank2s+γ,respectively.Finally,wehaveobtainedsimplerepresentationofenumerationalformulasusingq-hypergeometricseries.KeywordsSymmetricmatrixequation,Singularort

6、hogonalspace,q-hypergeometricseries1991MRSubjectClassification05E15ChineseLibraryClassificationO151=:gqrN~yp>Q?
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`2Oqn9&a

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G-δ=0,1

10、2Q∅,:δ=0m,1∆=

11、z,:δ=1m,(2)
1,:δ=2m,−zνQ∆T$S2ν+δ,∆,Sn,2γ+δ,∆>jynEmTZ`mA>mr2ν+δ,>ν,∆>$A>jynEmTFqd;KmG$&a