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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Goppa code ： ウィキペディア英語版 Goppa code In mathematics, an algebraic geometric code (AG-code), otherwise known as a Goppa code, is a general type of linear code constructed by using an algebraic curve $X$ over a finite field $\backslash mathbb\_q$. Such codes were introduced by Valerii Denisovich Goppa. In particular cases, they can have interesting extremal properties. They should not be confused with Binary Goppa codes that are used, for instance, in the McEliece cryptosystem. ==Construction== Traditionally, an AG-code is constructed from a non-singular projective curve X over a finite field $\backslash mathbb\_q$ by using a number of fixed distinct $\backslash mathbb\_q$ -rational points :$\backslash mathcal$:= ⊂ X ( $\backslash mathbb\_q$) on X. Let G be a divisor on X, with a support that consists of only rational points and that is disjoint from the $P\_i$'s. Thus $\backslash mathcal$ ∩ supp(G) = Ø By the Riemann-Roch theorem, there is a unique finite-dimensional vector space, $L(G)$, with respect to the divisor G. The vector space is a subspace of the function field of X. There are two main types of AG-codes that can be constructed using the above information. 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「Goppa 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.