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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 Preparata code ： ウィキペディア英語版 Preparata code In coding theory, the Preparata codes form a class of non-linear double-error-correcting codes. They are named after Franco P. Preparata who first described them in 1968. Although non-linear over GF(2) the Preparata codes are linear over Z4 with the Lee distance. ==Construction== Let ''m'' be an odd number, and $n\; =\; 2^m-1$. We first describe the extended Preparata code of length $2n+2\; =\; 2^$: the Preparata code is then derived by deleting one position. The words of the extended code are regarded as pairs (''X'', ''Y'') of 2''m''-tuples, each corresponding to subsets of the finite field GF(2''m'') in some fixed way. The extended code contains the words (''X'', ''Y'') satisfying three conditions # ''X'', ''Y'' each have even weight; # $\backslash sum\_\; x\; =\; \backslash sum\_\; y;$ # $\backslash sum\_\; x^3\; +\; \backslash left(\backslash sum\_\; x\backslash right)^3\; =\; \backslash sum\_\; y^3.$ The Peparata code is obtained by deleting the position in ''X'' corresponding to 0 in GF(2''m''). 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「Preparata 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.