小維數(shù)和小權數(shù)的MDS碼.pdf

1、上海大學碩士學位論文小維數(shù)和小權數(shù)的MDS碼姓名：王德秀申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：楊建生20080501AbstractCodeswithd=n—k1arecalledm戚mumdistanceseparablecodes，orMDScodesforshortFixedparametersn，k，MDScodeshavethema硒m以correctingabilityanditsweightdistributionis

2、completelyfixedIfacodeCovertheqaryalphabetA一o，1，2，，口一1)isanMDScodeoflengthn，dimsion七，andminimumdistanced，thenanyksymbolsofcodewordsmaybetakenasmessagesymbolsMDScodescanbeseparatedintolinearMDScodesandnonlinearMDScodesThe

3、investigationoflinearMDScodescanrecurtotheknowledgeofLinearAlgebra，F(xiàn)initeFields，F(xiàn)initeGeometries，andProjectivePlane，LinearCodes，andSOonSoitsinvestigationnlademoreachievementsthannonlinearMDScodesThenonlinearMDScodesareon

4、lyasetofsomecodeswithparametersn，q，k，andd=n一七1，andwithoutsystemicinvestigationmethodsSo，itsinvestigationismoredifficultythanlinearMDScodesGenerallythemaximalnumbernsuchthatthereexistsalinear【n，k，nk1】MDScodeoverF口willbede

5、notedbym口(I)，andMq(k)denotethemaximalnumbernsuchthatthereexistsannonlinear(n，礦，n—k1)MDScodeoverqaryalphabetAClearlymg(七)≤^毛(七)OneoftheproblemsonMDScodesistodeterminetheexactvalueof塢(后)andmq(k)ortoobtainboundsforthemInthi

6、spaper，westudythemaximallength塢(后)ofMDScodeswiththeparameterg，kByusingtheknowledgeofthecombinatoricsmethods，theHammingdistanceofcodes，theequivalenceofcodes，theweightfomualofMDScodes，mutuallyorthogonalLatinsquares，andthew

7、eightdistributionofMDScodes，andsoon，weobtainannewupperboundformulaof塢(七)is鴆(七)≤L(q一1，七)k1，especiallyweobtainthat鴆(6)=8，鴆(口)=g1，andMd3)≤g1(qisodd)，Mq(q一1)≤q1(gisodd)，塢(口一1)≤q2(qisevenandq三4(rood6))KeywordsErrorCorrectingC