简介：C是一[n，k，d]q在\mathbbFq\mathbb上的线性代码{F}_q。并且s(C)=n+1kd是C的单条缺点。有s(C)=的AnMDS代码C0广泛地被学习了。最近，有s(C)=s(C)的near-MDS代码C=1被许多学者学习，在C表示C的双代码的地方。这份报纸与s(C)=s(C)专注于线性代码C=2，并且作者把它称为NNMDS代码。NNMDS代码的一系列见条件被介绍。并且作者在一些NNMDS代码上给上面的界限。在最后，NNMDS的一些例子被给。

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简介：在有限领域上的排列代码被介绍，为自我双的排列代码的存在或不存在的一些条件被获得。

简介：The’polarcoding’proposedbyDr.Arkancanachievethesymmetriccapacityofbinary-inputdiscretememorylesschannels(B-DMC).ThegeneratormatrixofpolarcodesisGN=BNFnforN=2n,BNwasapermutationmatrix.Inthearticleitwasrealizedwithaninterleaver,sothematrixproductionofGNwasavoided;thenthegeneratormatrixwasjustdeterminedbythematrixFnwhichwasconstructedwiththreesub-matrixesofFn-1andone2N-1orderzeromatrix,itwasdealwithfastHadamardtransform(FHT)algorithm.Thecomplexityofthenewschemewasreducedsharply,andaniterativealgorithmalsocanbeused.TheexampleshowedthatwhenN=8,complexityoftheencodingschemewasjust16whichisobviouslylessthanthatoforiginalencodingscheme36.

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简介：量退化代码可以改进量能力的哈希界限。我们建议退化代码从二可着色的图导出的量的一个家庭。代码的协调信息是为动摇隧道作为隧道噪音的一个函数获得的经分解。我们发现比重复代码的有更高的噪音阀值的新代码。

简介：ByapplyingaresultfromgeometricGoppacodes,duetoH.Schtenoth,thetruedimensionofcertainalternantcodesiscalculated.Theresultsleadinmanycasestoanimprovementoftheusuallowerboundforthedimension.

简介：Anoverviewispresentedonthestatusofstudiesonmultiplecodesingeneticsequences.Indirectly,theexistenceofmultiplecodesisrecognizedintheformofseveralrediscoveriesofSecondGeneticCodethatisdifferenteachtime.Aduecreditisgiventoearlierseminalworkrelatedtothecodesoftenneglectedinliterature.Thelatestdevelopmentsinthefieldofchromatincodearediscussed,aswellasperspectivesofsingle-baseresolutionstudiesofnucleosomepositioning,includingrotationalsettingofDNAonthesurfaceofthehistoneoctamers.

简介：Trellisstructuresofblockcodesarediscussed.L-sectiontrellisstructuresofsomeBCHcodesarepresented.AfastmaximumlikelihooddecodingalgorithmforBCHcodesisproposedcorrespondingly,thedecodingproblemofq-aryimagesofqm-aryblockcodesisalsodiscussed.Thedirect-sumpartitionandtheassociateddecodingalgorithmsaregivenfortheimages.

简介：Inthispaper,thequaternaryDelsarte-GoethalscodeDG(m，δ）anditsdualcodeGD(m,δ)arediscussed.ThetypeandthetracerepresentationaregivenforDG\(m,δ),whilethetypeandtheminimumLeeweightaredeterminedforGD(m,δ),TheshortenedcodesofDG(m,δ)andGD(m,δ),areprovedtobeZZ4-cyclic.ThebinaryimageofDG(m,δ)isprovedtobethebinaryDelsarte-GoethalscodeDG((m+1,δ),andtheessentialdifferencebetweenthebinaryimageofGD(m,δ)andthebinaryGoethals-DelsartecodeGD((m+1,δ)isexhibited.Finally,thedecodingalgorithmsofDG(m,δ)andGD(m,δ)arediscussed.

简介：Low-DensityParity-Check(LDPC)codeisoneofthemostexcitingtopicsamongthecodingtheorycommunity.Itisofgreatimportanceinboththeoryandpracticalcommunicationsovernoisychannels.ThemostadvantageofLDPCcodesistheirrelativelylowerdecodingcomplexitycomparedwithturbocodes,whilethedisadvantageisitshigherencodingcomplexity.Inthispaper,anewap-proachisfirstproposedtoconstructhighperformanceirregularsystematicLDPCcodesbasedonsparsegeneratormatrix,whichcansignificantlyreducetheencodingcomplexityunderthesamede-codingcomplexityasthatofregularorirregularLDPCcodesdefinedbytraditionalsparseparity-checkmatrix.Then,theproposedgenerator-basedsystematicirregularLDPCcodesareadoptedascon-stituentblockcodesinrowsandcolumnstodesignanewkindofproductcodesfamily,whichalsocanbeinterpretedasirregularLDPCcodescharacterizedbygraphandthusdecodediteratively.Finally,theperformanceofthegenerator-basedLDPCcodesandtheresultantproductcodesisinvestigatedoveranAdditiveWhiteGaussianNoise(AWGN)andalsocomparedwiththeconventionalLDPCcodesunderthesameconditionsofdecodingcomplexityandchannelnoise.

简介：Thispaperisdevotedtodeterminingthestructuresandpropertiesofone-Leeweightcodesandtwo-LeeweightprojectivecodesCk1,k2,k3overpIF+vIFpwithtypep2k1pk2pk3.Theauthorsintroduceadistance-preservingGraymapfrom(IFp+vIFp)nto2np.BytheGraymap,theauthorsconstructafamilyofoptimalone-Hammingweightp-arylinearcodesfromone-LeeweightcodesoverIFp+vIFp,whichattainthePlotkinboundandtheGriesmerbound.Theauthorsalsoobtainaclassofoptimalp-arylinearcodesfromtwo-LeeweightprojectivecodesoverIFp+vIFp,whichmeettheGriesmerbound.

简介：LetRbeafinitechainringwithmaximalidealγandresiduefieldF,andletγbeofnilpotencyindext.ToeverycodeCoflengthnoverR,atowerofcodesC=(C:γ0)(C:γ)(C:γi)(C:γt-1)canbeassociatedwithC,whereforanyr∈R,(C:r)={e∈Rn|re∈C}.UsinggeneratorelementsoftheprojectionofsuchatowerofcodestotheresiduefieldF,wecharacterizecycliccodesoverR.ThischaracterizationturnstheconditionforcodesoverRtobecyclicintooneforcodesovertheresiduefieldF.Furthermore,weobtainacharacterizationofcycliccodesovertheformalpowerseriesringofafinitechainring.

简介：Afamilyofauthenticationcodeswitharbitrationisconstructedfromunitarygeome-try,theparametersandtheprobabilitiesofdeceptionsofthecodesarealsocomputed.Inaspe-cialcaseaperfectauthenticationcodewitharbitrationisohtalned.

简介：Inthispaper,onlynarrow-senseprimitiveBCHcodesoverGF(q)areconsidered.Aformula,thatcanbeusedinmanycases,isfirstpresentedforcomputingthedimensionofBCHcodes.ItimprovestheresultgivenbyMacWilliamsandSloanein1977.AnewmethodforfindingthedimensionofalltypesofBCHcodesisproposed.Insecondpart,itisprovedthattheBCHboundistheleaderofsomecyclotomiccoset,andweguessthattheminimumdistanceforanyBCHcodeisalsotheleaderofsomecyclotomiccoset.

简介：ThisnotedescribesthemodificationsoftheBESofflinedatareconstructioncodesfromtheHP-UNIXtoPCLINUXplatform.Themainchangesofthecodesandtheresultscompairsonwiththatofbeforemodificationsarepresented.

简介：AclassofGoppacodesisconstructedbyusingArtin-Schreierfunctionfields,ofwhichthenumberofprimedivisorsofdegreeoneisobtainedforsomecases,andtheirminimumdistance,dualityandself-dualityarediscussed.AtlastthesubfieldsubcodeofArtin-Schreiercodeisinvestigated,thetruedimensionundercertainconditionsisgivenandthecoveringradiusandminimumdistanceareestimated.

简介：Anewclassofmultilength,constant-weightandtwo-dimensionalmultiwavelengthopticalorthogonalcode(2DMWOOCs)withlargecapacityandgoodcorrelationpropertiesisconstructedbasedonmultilengthone-dimensional(1D)OOCs.TheperformanceofthesenewMWOOCsinanOCDMAnetworkwithdouble-servicesisanalyzed.Theresultshowsthatmediawiththeshortercodewordperformsmuchbetterthanthemediawithlongercodeword,andOCDMAsystemwiththesenewmultilengthMWOOCsperformswell.ThesefeaturesallowmultimediatransmissionoflargecapacityinOCDMAsystem.

简介：Anovelschemeemployinglow-densityparity-check(LDPC)codesinatmosphericopticalcommunicationsystemisproposed.Wedeploycoherentdetectionatthereceivingsideintheproposedscheme.Toreducebiterrorrate(BER)andenhancethesystemperformance,LDPCcodesareexploitedandcoherentreceiverisusedtoimprovethereceivingsensitivity.Experimentsareimplementedtoevaluatetheperformanceofthetransmissionsystem.Theatmosphericchannelattenuationsaresetto20-30dB/km.ThecoherentdetectionwithLDPCcodescanreducethereceivedpowerrequirementby~4dBmattheBERof10-9.