四元環(huán)上的GH-碼.pdf

1、福建師范大學(xué)碩士學(xué)位論文四元環(huán)上的GH_碼TheGeneralizedHcodeOverQuateraaryRings林新棋學(xué)科專(zhuān)業(yè)：基礎(chǔ)報(bào)學(xué)研究方向；蛆臺(tái)數(shù)學(xué)指導(dǎo)教師t張勝元科教授申請(qǐng)學(xué)位坦別理半碩士№女女日∞墊韭—生j—a女目^：——《#日Ⅻi業(yè)ijL—且#mi日☆#l』t且越直m＆4口扭皿盟盞2i呈＆Ⅻ十日mz!蛆ij二—且AbstractLetGbeallelementaryAbelian2_group，F(xiàn)nfinitefiel

2、dofcharacteristic2，F(xiàn)GthecorrespondinggroupalgebraCamion(1979)introducedaspecialclassofAbeliancodeswhicharethenreferredto∞HcodesThesecodesareprovedtobeselfdualAndthataHcodeisdoublyevenselfdualcode(TypeIIcode、ifandonlyifth

3、eHammingweightofitsgeneratingelementisamultipleof4Bhattacharya(1984)definedageneralizedHcode(GHcode)，inwhichtheelementaryAbelian2groupisreplacedbyanAbeliangroupofevenorderHealsopointedouttheprojectivekernelofaGHcodeissim

4、ilartothatofaHcodeButaGHcodeisnotnecessarilyselfdualItWeiandLZhu(1996)gavenecessaryandsufficientconditionsforaGH_codetobedoublyevenselfdualbymeansofGHsetWhenthefinitefieldFisnotF2，theyalsopointedoutthataGHcodeisnotaTypeI

5、Icode(underHammingweights)InthisthesisweconsiderGHcodesoverquaternaryringsThisthesisisdividedinto4sectionsInsection1weintroducesomecorrelativebackgroundofourmaincontentsandresultsThenwedefinethegeneralizedH_codesoveraqua

6、ternaryring，andgivenecessaryandsufficientconditionsforaGHcodetobeselfdualoratypeIIcodeThereare4differentquaternarycommutativeringswithidentity：OF(4)，毋“兄，瑪“F2andZ4Insections2，3and4，weconsiderGHcodesoverOF(4)，F(xiàn)2u足andF2vF2r

7、espectivelyintroducethedefinitionofcorrespondingGHsetpairs，andgivenecessaryandsufficientconditionsforaGHcodetobeatypeIIcode(underLeeweights)Attheendofsection4，weprovethatthereisnoGHcodeoverZdtobeselfdualKeywords：linearco