翻訳と辞書 Words near each other ・ Hammoon ・ Hammoor ・ Hammoth-dor ・ Hammou Boutayeb ・ Hammick baronets ・ Hammick reaction ・ Hammie Nixon ・ Hammigi ・ Hammil, California ・ Hammill ・ Hamming ・ Hamming bound ・ Hamming code ・ Hamming distance ・ Hamming graph ・ Hamming scheme ・ Hamming space ・ Hamming weight ・ Hamming(7,4) ・ Hammink ・ Hamminkeln ・ Hamminkeln railway station ・ Hammir Dev Chauhan ・ Hammir Singh ・ Hammock ・ Hammock (band) ・ Hammock (disambiguation) ・ Hammock (ecology) ・ Hammock activity ・ Hammock camping Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hamming scheme ： ウィキペディア英語版 Hamming scheme The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory.〔P. Delsarte and V. I. Levenshtein, “Association schemes and coding theory,“ ''IEEE Trans. Inform. Theory'', vol. 44, no. 6, pp. 2477–2504, 1998.〕〔P. Camion, "Codes and Association Schemes: Basic Properties of Association Schemes Relevant to Coding," in ''Handbook of Coding Theory'', V. S. Pless and W. C. Huffman, Eds., Elsevier, The Netherlands, 1998.〕〔F. J. MacWilliams and N. J. A. Sloane, ''The Theory of Error-Correcting Codes'', Elsevier, New York, 1978.〕 In this scheme $X=\backslash mathcal^n$, the set of binary vectors of length $n$, and two vectors $x$, $y\backslash in\; \backslash mathcal^n$ are $i$-th associates if they are Hamming distance $i$ apart. Recall that an association scheme is visualized as a complete graph with labeled edges. The graph has $v$ vertices, one for each point of $X$, and the edge joining vertices $x$ and $y$ is labeled $i$ if $x$ and $y$ are $i$-th associates. Each edge has a unique label, and the number of triangles with a fixed base labeled $k$ having the other edges labeled $i$ and $j$ is a constant $c\_$, depending on $i,j,k$ but not on the choice of the base. In particular, each vertex is incident with exactly $c\_=v\_$ edges labeled $i$; $v\_$ is the valency of the relation $R\_$. The $c\_$ in a Hamming scheme are given by : $c\_\; =\; \backslash begin$ \dbinom}\dbinom}, & \text i+j-k \text \\ \;\;\;\;\;\;\;\;\;\;0\;\;\;\;\;\;\;\;\;\;\;,\;\; & \text i+j-k \text \end Here, $v=\backslash left|X\backslash right|=2^$ and $v\_=\backslash binom$. The matrices in the Bose-Mesner algebra are $2^\backslash times\; 2^$ matrices, with rows and columns labeled by vectors $x\backslash in\; \backslash mathcal^$. In particular the $\backslash left(x,y\backslash right)$-th entry of $D\_$ is $1$ if and only if $d\_(x,y)=k$. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hamming scheme」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.