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1、AlgorithmsandComputationinMathematics•Volume17EditorsArjehM.CohenHenriCohenDavidEisenbudBerndSturmfelsGabrieleNebeEricM.RainsNeilJ.A.SloaneSelf-DualCodesandInvariantTheoryWith10Figuresand34TablesABCAuthorsGabrieleNebeNeilJ.A.SloaneLehrstuhlDfürMathematikInternetandNetworkSystemsR

2、esearchRheinisch-WestfälischeAT&TShannonLabsTechnischeHochschuleAachen180ParkAvenueTemplergraben64FlorhamPark,NJ07932-097152062AachenUSAGermanye-mail:njas@research.att.come-mail:nebe@math.rwth-aachen.deEricM.RainsDepartmentofMathematicsUniversityofCaliforniaatDavis1ShieldsAveDavi

3、s,CA95616USAe-mail:rains@math.ucdavis.eduLibraryofCongressControlNumber:2005937507MathematicsSubjectClassification(2000):94B05,94B60,13A50,16P10,20G05;15A66,16D90,68Q99,81R99ISSN1431-1550ISBN-103-540-30729-XSpringerBerlinHeidelbergNewYorkISBN-13978-3-540-30729-7SpringerBerlinHeide

4、lbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispubli

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cSpringer-VerlagBerlinHeidelberg2006PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgen

7、eraluse.Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1158717017/TechBooks543210PrefaceThisbookhastwogoals.Ontheonehanditdevelopsacompletelynewuni-fyingtheoryofself-dualcodesthatenablesus

8、toproveafar-reachinggeneral-izationofGle