域F-,q-上的[q-1,k]循環(huán)碼的研究.pdf

1、中山大學碩士學位論文域F上的[q1k]循環(huán)碼的研究姓名：朱書威申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：胡國權(quán)20050602中山大學碩士學位論文Theresearchon[qlk】CycliccodesovereqMajor：AppliedAathematicsName：ZhuShuⅥ，ciSuperwisor：HuGuoQuanAbstractTheresearchOnerror—correctingabilityofacodeis

2、tOanalysistherelationshipbetweencodelengthn，informationbitkandminimumdistancedThisworkistostudytherelationshipbetweendandn，kwheren，kisfixofcycliccodesover‘F：isisomorphictotheresidueclassringF[xl／xn一1(consideredonlyasanad

3、ditivegroup)，usuallywestudycycliccodesbymeansofpolynomialCycliccodeisaprincipalideaofF[xl／x4—1，s0thereexistangeneratorpolynomialg(x)whichgeneratesthecycliccodeItisknownthattheminimumdistanceofacycliccodehascloserelations

4、hipwiththerootsofitsgeneratorpolynomialForcycliccodesarespecialsubspacesofalinearspaceWehopetOconstructabasisforacyclicsubspaceBymeansoftheMattsonSolomonpolynomial，weconstructabasisforaInk】cyclicsubspaceover只wheren。q一1In

5、theorem7，weshowthatthereexists砷，女，_n】cyclicSUbspaces，ifkInAndtheminimum庀distanceforanyIn，七】cyclicsubspaceisnolessthan_nEspeciallyifqisodd，托thereexists【口一1，!王，2】cyclicsubspacecLetq—，。。Thentherate。fciS三，buttne瓶tance。rc趣。n，