翻訳と辞書 Words near each other ・ Elias and companions ・ Elias Andersson ・ Elias Andra ・ Elias Anton Cappelen Smith ・ Elias Arnér ・ Elias Ashmole ・ Elias Aslaksen ・ Elias Atallah ・ Elias Atmatsidis ・ Elias Avery Lowe ・ Elias B. Caldwell ・ Elias B. D. Ogden ・ Elias B. Holmes ・ Elias Baeck ・ Elias Bandak ・ Elias Bassalygo bound ・ Elias Bazzi ・ Elias Bernard Koopman ・ Elias Bernstein Intermediate School ・ Elias Bjuhr ・ Elias Blix ・ Elias Bogan ・ Elias Bongmba ・ Elias Bou Saab ・ Elias Boudinot ・ Elias Boudinot (Cherokee) ・ Elias Boudinot (disambiguation) ・ Elias Breeskin ・ Elias Brendle Monteith House and Outbuildings ・ Elias Brenner 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 Elias Bassalygo bound ： ウィキペディア英語版 Elias Bassalygo bound The Elias-Bassalygo bound is a mathematical limit used in coding theory for error correction during data transmission or communications. The properties of the Elias-Bassalygo bound are defined, below, using mathematical expressions. == Definition == Let $C$ be a $q$-ary code of length $n$, i.e. a subset of $()^n$. (Each $q$-ary block code of length $n$ is a subset of the strings of $\backslash mathcal\_q^n\backslash text$ where the alphabet set $\backslash mathcal\_q$ has $q$ elements). Let $R$ be the ''rate'' of $C$ and $\backslash delta$ (delta) be the ''relative distance''. Let $B\_q(\backslash boldsymbol,\; \backslash rho\; n)\; =\backslash ,\; \backslash boldsymbol)\; \backslash le\; \backslash rho\; n\; \backslash \}$ be the ''Hamming ball'' of radius $\backslash rho\; n$ centered at $\backslash boldsymbol$. Let $Vol\_q(\backslash boldsymbol,\; \backslash rho\; n)\; =\; |B\_q(\backslash boldsymbol,\; \backslash rho\; n)|$ be the ''volume'' of the Hamming ball of radius $\backslash rho\; n$. It is obvious that the volume of a Hamming Ball is translation-invariant, i.e. irrelevant with position of $\backslash boldsymbol$. In particular, $|B\_q(\backslash boldsymbol,\; \backslash rho\; n)|\; =|B\_q(\backslash boldsymbol,\; \backslash rho\; n)|$ . With large enough $n$, the ''rate'' $R$ and the ''relative distance'' $\backslash delta$ satisfies the ''Elias-Bassalygo bound:'' $R\; \backslash le\; 1\; -\; H\_q(\; J\_q(\backslash delta))+o(1)\backslash text$ where : $H\_q(x)\backslash equiv\_\; \backslash text\; -x\backslash cdot\backslash log\_q$ is the ''q''-ary entropy function and : $J\_q(\backslash delta)\; \backslash equiv\_\; \backslash text\; \backslash left(1-\backslash right)\backslash left(1-\backslash sqrt\backslash right)$ is a function related with Johnson bound. 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「Elias Bassalygo bound」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.