翻訳と辞書 Words near each other ・ Juste Lisch ・ Juste milieu ・ Juste Olivier ・ Juste un instant ・ Juste Une Ligne Bleue ・ Juste une photo de toi ・ Juste-Aurèle Meissonnier ・ Juste-Charles de Fay de La Tour-Maubourg ・ Justel, Zamora ・ Justellus ・ Justen Ericksen ・ Justen Glad ・ Justen Naughton ・ Juster ・ Justerini & Brooks ・ Justesen code ・ JustFab ・ JustFoodERP ・ JustGarciaHill.org ・ JustGive ・ Justgiving ・ Justi Baumgardt ・ Justian ・ JUSTICE ・ Justice ・ Justice & Kaos ・ Justice (1914 film) ・ Justice (1917 film) ・ Justice (1954 TV series) ・ Justice (1971 TV series) 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 Justesen code ： ウィキペディア英語版 Justesen code In coding theory, Justesen codes form a class of error-correcting codes that have a constant rate, constant relative distance, and a constant alphabet size. Before the Justesen code was discovered, no code was known that had all of these three parameters as a constant. Subsequently, other codes with this property have been discovered, for example expander codes. These codes have important applications in computer science such as in the construction of small-bias sample spaces. Justesen codes are derived as the code concatenation of a Reed–Solomon code and the Wozencraft ensemble. The Reed–Solomon codes used achieve constant rate and constant relative distance at the expense of an alphabet size that is ''linear'' in the message length. The Wozencraft ensemble is a family of codes that achieve constant rate and constant alphabet size, but the relative distance is only constant for most of the codes in the family. The concatenation of the two codes first encodes the message using the Reed–Solomon code, and then encodes each symbol of the codeword further using a code from the Wozencraft ensemble – using a different code of the ensemble at each position of the codeword. This is different from usual code concatenation where the inner codes are the same for each position. The Justesen code can be can constructed very efficiently using only logarithmic space. ==Definition== Justesen code is concatenation code with different linear inner codes, which is composed of an $(N,K,D)\_$ outer code $C\_$ and different $(n,k,d)\_q$ inner codes $C\_^i$, $1\; \backslash le\; i\; \backslash le\; N$. More precisely, the concatenation of these codes, denoted by $C\_\; \backslash circ\; (C\_^1\; ,...,C\_^N\; )$, is defined as follows. Given a message $m\; \backslash in\; ()^K$, we compute the codeword produced by an outer code $C\_$: $C\_(m)\; =\; (c\_1,c\_2,..,c\_N)$. Then we apply each code of N linear inner codes to each coordinate of that codeword to produce the final codeword; that is, $C\_\; \backslash circ\; (C\_^1,..,C\_^N)(m)\; =\; (C\_^1(c\_1),C\_^2(c\_2),..,C\_^N(c\_N))$. Look back to the definition of the outer code and linear inner codes, this definition of the Justesen code makes sense because the codeword of the outer code is a vector with $N$ elements, and we have $N$ linear inner codes to apply for those $N$ elements. Here for the Justesen code, the outer code $C\_$ is chosen to be Reed Solomon code over a field $\backslash mathbb\_$ evaluated over $\backslash mathbb\_-\backslash$ of rate $R$, $0$ < $R$ < $1$. The outer code $C\_$ have the relative distance $\backslash delta\_\; =\; 1\; -\; R$ and block length of $N\; =\; q^k-1$. The set of inner codes is the Wozencraft ensemble $\backslash \; \_^$ * }. 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「Justesen code」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.