{"id":894,"date":"2019-02-17T08:48:57","date_gmt":"2019-02-16T23:48:57","guid":{"rendered":"http:\/\/arisasuper.com\/?p=894"},"modified":"2019-10-22T21:57:37","modified_gmt":"2019-10-22T12:57:37","slug":"%e3%83%a2%e3%83%b3%e3%83%86%e3%82%ab%e3%83%ab%e3%83%ad%e6%b3%95%e3%81%a8%e3%82%b7%e3%83%9f%e3%83%a5%e3%83%ac%e3%83%bc%e3%82%b7%e3%83%a7%e3%83%b3","status":"publish","type":"post","link":"https:\/\/arisasuper.com\/?p=894","title":{"rendered":"\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3068\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3"},"content":{"rendered":"<p><a href=\"https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-895 aligncenter\" src=\"https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001-210x300.jpg\" alt=\"\" width=\"210\" height=\"300\" srcset=\"https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001-210x300.jpg 210w, https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001-768x1097.jpg 768w, https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001-717x1024.jpg 717w, https:\/\/arisasuper.com\/wp-content\/uploads\/2019\/02\/IMG_20190217_0001.jpg 1744w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/a><\/p>\n<p><span style=\"font-size: 14pt;\">\u300c\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3068\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u300d\u3000\u6d25\u7530\u5b5d\u592b\u8457<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u3053\u306e\u672c\u306ep36\u30017\u884c\u76ee\uff5ep37\u30012\u884c\u76ee\u306f\u3001M\u7cfb\u5217\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u3010\uff21\u3011\u6700\u5927\u5468\u671f\u5217\uff08M\u7cfb\u5217\uff09<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u30ac\u30ed\u30a2\u4f53GF(q)\u306en\u6b21\u591a\u9805\u5f0ff(x)\u304c\u539f\u59cb\u7684(primitive)\u3067\u3042\u308b\u3068\u304d\u3001\u6700\u5927\u5468\u671fq^n-1\u3092\u3082\u3064\u6570\u5217\u3092f(x)\u3088\u308a\u751f\u6210\u3067\u304d\u308b\u3002<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">(\u4e2d\u7565)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">GF(2)\u3067\u8981\u7d20{0,1}\u306e\u307f\u3092\u5bfe\u8c61\u3068\u3059\u308b\u3068\u304d\u3001<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u3042\u308b\u56fa\u5b9a\u3057\u305fm\u306b\u3064\u3044\u3066<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">s[0]=a[0]\u3001s[1]=a[1]\u3001\u30fb\u30fb\u30fb\u3001s[m-1]=a[m-1]\u3000\u3000\uff08[\u30fb]\u306f\u6dfb\u3048\u5b57\u3092\u8868\u3059\u3053\u3068\u3068\u3057\u307e\u3059\u3002\uff09<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u3092\u4e0e\u3048\u308b\u3068\u3001mod2\u306e\u7dda\u5f62\u6f38\u5316\u5f0f<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">f[0]s[i]+f[1]s[i-1]+\u30fb\u30fb\u30fb+f[m]s[i-m]=0\u3000\u3000(mod2)\u3000\u3000(2\uff6527)<\/span><br \/>\n<span style=\"font-size: 14pt;\">\uff08i=m\u3001m+1\u3001m+2\u3001\u30fb\u30fb\u30fb\u3000;\u3000f[m]\u22600\u3001f[0]\u22600\uff09<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3088\u308a\u3001\u8981\u7d20{0,1}\u306e\u7121\u9650\u6570\u5217<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">s={s[0]\u3001s[1]\u3001s[2]\u3001\u30fb\u30fb\u30fb\u3001s[m-1]\u3001s[m]\u3001\u30fb\u30fb\u30fb}\u3000\u3000\u3000\u3000(2\uff6528)<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u304c\u9806\u6b21\uff08\u518d\u5e30\u7684\u306b\uff09\u5f97\u3089\u308c\u308b\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3053\u3053\u3067<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">s[j]\u2208GF(2)\u3001f[k]\u2208GF(2)\u3000\uff08j=0\u30011\u30012\u3001\u30fb\u30fb\u30fb\u3001m\u3001m+1\u3001\u30fb\u30fb\u30fb; k=0\u30011\u30012\u3001\u30fb\u30fb\u30fb\u3001m\uff09<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u3059\u306a\u308f\u3061\u3001\u3068\u3082\u306b\u30010\u307e\u305f\u306f1\u306e\u6570\u3067\u3042\u308b\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">(2\uff6527)\u306b\u5bfe\u3057\u3001\u591a\u9805\u5f0f<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">f(x)=f[0]+f[1]x+f[2]x^2+\u30fb\u30fb\u30fbf[m]x^m\u3000\u3000\uff08f[0]=f[m]=0\uff09\u3000\u3000(2\uff6529)<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u3092\u305d\u306e\u7279\u6027\u591a\u9805\u5f0f\u3068\u3044\u3044\u3001\u7121\u9650\u6570\u5217(2\uff6528)\u306f\u3001\u591a\u9805\u5f0f(2\uff6529)\u3088\u308a\u751f\u6210\u3055\u308c\u308b\u3068\u3044\u3046\u3002<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e\uff5e<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3068\u3053\u308d\u304c\u3001(2\uff6527)\u306e\u7dda\u5f62\u6f38\u5316\u5f0f\u3067\u306f\u3001M\u7cfb\u5217\u306f\u751f\u6210\u3055\u308c\u307e\u305b\u3093\u3002<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u4ee5\u4e0b\u306e\u6f38\u5316\u5f0f\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u306e\u3067\u3059\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">f[0]s[i-m]+f[1]s[i-m+1]+f[2]s[i-m+2]+\u30fb\u30fb\u30fb+f[m-1]s[i-1]+f[m]s[i]=0\u3000\u3000\u3000(\uff71)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3053\u306e\u672c\u306e\u521d\u7248\u306f\u3000\u662d\u548c44\u5e746\u670820\u65e5\u3001\u6539\u8a02\u7248\u306f\u3000\u662d\u548c52\u5e7411\u670815\u65e5\u3001\u3000\u6539\u8a02\u7248\u7b2c3\u5237\u304c\u662d\u548c55\u5e7410\u670830\u65e5\u306b\u3067\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u521d\u7248\u306f50\u5e74\u524d\u306b\u3001\u6539\u8a02\u7248\u7b2c3\u5237\u3067\u308240\u5e74\u524d\u306e\u3082\u306e\u3067\u3059\u3002<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u4eca\u3055\u3089\u6c17\u3065\u3044\u3066\u3082\u3001\u3069\u3046\u306b\u3082\u306a\u3089\u306a\u3044\u3067\u3057\u3087\u3046\u3057\u3001\u3053\u3093\u306a\u53e4\u3044\u672c\u3067\u52c9\u5f37\u3059\u308b\u3059\u308b\u4eba\u3082\u3001\u3082\u306f\u3084\u3044\u306a\u3044\u3067\u3057\u3087\u3046\u3057\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u305d\u3082\u305d\u3082\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3092\u4f7f\u3046\u306e\u3067\u3042\u308c\u3070\u3001\u7dda\u5f62\u6f38\u5316\u5f0f\u3088\u308a\u3001\u7279\u6027\u591a\u9805\u5f0f\u304b\u3089\u306eM\u7cfb\u5217\u751f\u6210\u304c\u672c\u6d41\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002<\/span><br \/>\n<span style=\"font-size: 14pt;\">\u8ab0\u3082\u7dda\u5f62\u6f38\u5316\u5f0f\u3092\u4f7f\u3063\u3066\u6570\u5217\u3092\u8a08\u7b97\u3057\u3066\u307f\u3088\u3046\u306a\u3069\u3068\u306f\u601d\u308f\u306a\u304b\u3063\u305f\u306e\u3067\u3057\u3087\u3046\u3002\u300c\u3075\u3080\u3075\u3080\u300d\u3068\u4e00\u77a5\u3057\u3066\u6b21\u306e\u6bb5\u968e\u306b\u79fb\u884c\u3057\u3066\u3044\u3063\u305f\u306e\u3067\u3057\u3087\u3046\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">50\u5e74\u7d4c\u3063\u3066\u3001\u3088\u3046\u3084\u304f\u7269\u597d\u304d\u304c\u73fe\u308c\u3066\u3001\u8a08\u7b97\u3057\u3066\u307f\u305f\u3089\u300c\u3042\u308c\uff1f\u300d\u3063\u3066\u306a\u3053\u3068\u306b\u306a\u3063\u305f\u306e\u3067\u3059\u306d\u3002<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u30e1\u30c7\u30bf\u30b7\u3001\u30e1\u30c7\u30bf\u30b7\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3061\u306a\u307f\u306b\u3001<\/span><br \/>\n<span style=\"font-size: 14pt;\">m=5\u3001\u521d\u671f\u5024{11111}\u3001f[0]=f[2]=f[5]=1\u3001f[1]=f[3]=f[4]=0\u3000\u3068\u3057\u305f\u3068\u304d\u306b\u3001<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">(2\uff6527)\u3067\u7b97\u51fa\u3057\u305f\u6570\u5217\uff081\u5468\u671f\u5206\uff09\u306f\u3001<\/span><br \/>\n<span style=\"font-size: 14pt;\">s\u21921\u30011\u30011\u30011\u30011\u30010\u30010\u30011\u30011\u30010\u30011\u30010\u30011\u30011\u30011\u30010\u30011\u30011\u30010\u30010\u30010\u30011\u30011\u30011\u30011\u30011\u30010\u30010\u30011\u30011\u30010\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u4e00\u65b9\u3001(\uff71)\u3067\u7b97\u51fa\u3057\u305f\u6570\u5217\uff081\u5468\u671f\u5206\uff09\u306f\u3001<\/span><br \/>\n<span style=\"font-size: 14pt;\">s\u21921\u30011\u30011\u30011\u30011\u30010\u30010\u30010\u30011\u30011\u30010\u30011\u30011\u30011\u30010\u30011\u30010\u30011\u30010\u30010\u30010\u30010\u30011\u30010\u30010\u30011\u30010\u30011\u30011\u30010\u30010\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3053\u308c\u3089\u3092\u3001\u672c\u66f8p39\u300112\u884c\u76ee\u306b\u4f8b\u3068\u3057\u3066\u793a\u3055\u308c\u3066\u3044\u308b\u539f\u59cb\u591a\u9805\u5f0f<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">f(x)=x^5+x^2+1\u3000\u3000\u3000\u3000(2\uff6533)<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u521d\u671f\u5024s[0]=s[1]=s[2]=s[3]=s[4]=1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u304b\u3089\u7b97\u51fa\u3055\u308c\u308b\u6700\u521d\u306e1\u5468\u671f\u5206\u306e\u6570\u5217<\/span><br \/>\n<span style=\"font-size: 14pt;\">s[i]\u21921\u30011\u30011\u30011\u30011\u30010\u30010\u30010\u30011\u30011\u30010\u30011\u30011\u30011\u30010\u30011\u30010\u30011\u30010\u30010\u30010\u30010\u30011\u30010\u30010\u30011\u30010\u30011\u30011\u30010\u30010\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3001(\uff71)\u304b\u3089\u7b97\u51fa\u3055\u308c\u305f\u6570\u5217\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">\u30e8\u30ab\u30c3\u30bf\u3001\u30e8\u30ab\u30c3\u30bf\u3002<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"\u3053\u306e\u672c\u306ep36\u30017\u884c\u76ee\uff5ep37\u30012\u884c\u76ee\u306f\u3001M\u7cfb\u5217\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u3010\uff21\u3011\u6700\u5927\u5468\u671f\u5217\uff08M\u7cfb\u5217\uff09 \u30ac\u30ed\u30a2\u4f53GF(q)\u306en\u6b21\u591a\u9805\u5f0ff(x)\u304c\u539f\u59cb\u7684(primitive)\u3067\u3042\u308b\u3068\u304d\u3001\u6700\u5927\u5468\u671fq^n-1\u3092\u3082\u3064\u6570\u5217\u3092f(x)\u3088\u308a\u751f\u6210\u3067\u304d\u308b\u3002","protected":false},"author":1,"featured_media":1083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18],"tags":[],"class_list":["post-894","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book"],"_links":{"self":[{"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/posts\/894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/arisasuper.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=894"}],"version-history":[{"count":9,"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/posts\/894\/revisions"}],"predecessor-version":[{"id":900,"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/posts\/894\/revisions\/900"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/arisasuper.com\/index.php?rest_route=\/wp\/v2\/media\/1083"}],"wp:attachment":[{"href":"https:\/\/arisasuper.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/arisasuper.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/arisasuper.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}