| ON THE EXPECTATION AND VARIANCE OF HAMMING DISTANCE BETWEEN TWO I.I.D RANDOM VECTORS |
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| 作者姓名： | 符方伟 沈世镒 |
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| 作者单位： | Department of Mathematics，Nankai University，Tianjin 300071，China |
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| 摘 要： | 1.IntroductionLetFZn={0,1}"beann-dimensionalvectorspaceoverthebinaryfieldFZ={0,1}.TheHammingdistancebetweentwovectorsx=(xl,'tx.)andy=(yi,'ty.)isthenumberofcoordinateswheretheydiffer,andisdenotedbydH(x,y),dH(X,y)=ZIXi~ail.i=1TheHammingweightofxisthenumberofnon-zerocoordinates,andisdenotedbyWH(x).ObviouslyAH(x)=dH(x,0),where0isthezerovector.Thescalarproductofxandyis(x,y)=xlyl ' xestinF2.ForasetAgFZn,IAIdenotesthecardinalityofA.TheaveragedistanceinAisdefinedby*Thisresearchissupp…
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| 收稿时间： | 31 July 1993 |
On the expectation and variance of hamming distance between two i.i.d random vectors |
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| Fangwei Fu,Shiyi Shen.ON THE EXPECTATION AND VARIANCE OF HAMMING DISTANCE BETWEEN TWO I.I.D RANDOM VECTORS[J].Acta Mathematicae Applicatae Sinica,1997,13(3):243-250. |
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| Authors: | Fangwei Fu Shiyi Shen |
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| Institution: | (1) Department of Mathematics, Nankai University, 300071 Tianjin, China |
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| Abstract: | By using the generalized MacWilliams theorem, we give new representations for expectation and variance of Hamming distance between two i.i.d random vectors. By using the new representations, we derive a lower bound for the variance, and present a simple and direct proof of the inequality of 1]. |
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| Keywords: | Hamming distance random vector expectation variance generalized MacWilliams theorem |
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