{"id":477241,"date":"2023-08-09T09:09:43","date_gmt":"2023-08-09T09:09:43","guid":{"rendered":""},"modified":"2024-07-01T04:50:32","modified_gmt":"2024-07-01T04:50:32","slug":"finite-field","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/ar\/wiki\/finite-field\/","title":{"rendered":"\u0645\u062c\u0627\u0644 \u0645\u062d\u062f\u0648\u062f"},"content":{"rendered":"<p>\u064a\u0639\u062f \u0627\u0644\u062d\u0642\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u060c \u0623\u0648 \u062d\u0642\u0644 \u062c\u0627\u0644\u0648\u0627\u060c \u062c\u0632\u0621\u064b\u0627 \u0644\u0627 \u064a\u062a\u062c\u0632\u0623 \u0645\u0646 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0645\u062c\u0631\u062f \u0627\u0644\u0630\u064a \u064a\u0644\u0639\u0628 \u062f\u0648\u0631\u064b\u0627 \u0645\u062d\u0648\u0631\u064a\u064b\u0627 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0633\u064a\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 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\u0627\u0644\u0625\u0636\u0627\u0641\u064a \u0648\u0627\u0644\u0645\u0636\u0627\u0639\u0641<\/strong>: \u0628\u0646\u064a\u0629 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0645\u0636\u0627\u0641\u0629 \u0644\u062d\u0642\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 q\u060c \u062d\u064a\u062b q = p^n\u060c \u0645\u062a\u0645\u0627\u062b\u0644 \u0644\u0644\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0644\u0646\u0633\u062e n \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u062f\u0648\u0631\u064a\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 p. \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0645\u0636\u0627\u0639\u0641\u0629 \u0644\u0644\u0639\u0646\u0627\u0635\u0631 \u063a\u064a\u0631 \u0627\u0644\u0635\u0641\u0631\u064a\u0629 \u0647\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u062f\u0627\u0626\u0631\u064a\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 q-1.<\/li>\n<li><strong>\u0648\u062c\u0648\u062f \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0641\u0631\u0639\u064a\u0629<\/strong>: \u0627\u0644\u062d\u0642\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0639\u0646\u0627\u0635\u0631 q = p^n \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u062d\u0642\u0644 \u0641\u0631\u0639\u064a \u0644\u0643\u0644 \u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u064a\u0647 d \u0639\u0644\u0649 n. \u0643\u0644 \u062d\u0642\u0644 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0641\u0631\u0639\u064a\u0629 \u0647\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u062c\u0645\u064a\u0639 \u062d\u0644\u0648\u0644 \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f x^(p^d) \u2013 x = 0.<\/li>\n<\/ol>\n<h2>\u0627\u0644\u062a\u0646\u0648\u0639 \u0641\u064a \u0627\u0644\u0648\u062d\u062f\u0629: \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629<\/h2>\n<p>\u064a\u062a\u0645 \u062a\u0635\u0646\u064a\u0641 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u062a\u0631\u062a\u064a\u0628\u0647\u0627\u060c \u0648\u0646\u0634\u064a\u0631 \u0639\u0627\u062f\u0629\u064b \u0625\u0644\u0649 \u062d\u0642\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0646 \u0627\u0644\u062a\u0631\u062a\u064a\u0628 q \u0628\u0627\u0644\u0631\u0645\u0632 GF(q). \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u064f\u0634\u0627\u0631 \u0625\u0644\u0649 \u0627\u0644\u062d\u0642\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0639\u0646\u0635\u0631\u064a\u0646 \u0628\u0640 GF(2)\u060c \u0648\u0628\u062b\u0644\u0627\u062b\u0629 \u0639\u0646\u0627\u0635\u0631 \u0628\u0627\u0644\u0631\u0645\u0632 GF(3)\u060c \u0648\u0647\u0643\u0630\u0627.<\/p>\n<p>\u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0642\u0648\u0629 \u0644\u0639\u062f\u062f \u0623\u0648\u0644\u064a\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0647\u064a GF(p)\u060c GF(p^2)\u060c GF(p^3)\u060c GF(p^4)\u060c \u0648\u0645\u0627 \u0625\u0644\u0649 \u0630\u0644\u0643. \u062d\u064a\u062b p \u0647\u0648 \u0639\u062f\u062f \u0623\u0648\u0644\u064a.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0645\u064a\u062f\u0627\u0646<\/th>\n<th>\u0627\u0644\u0645\u062c\u0627\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f (GF)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>2<\/td>\n<td>\u062c\u064a \u0625\u0641(2)<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u062c\u064a \u0625\u0641(3)<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>\u062c\u064a \u0625\u0641(4)<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>\u062c\u064a \u0625\u0641(5)<\/td>\n<\/tr>\n<tr>\n<td>\u0635<\/td>\n<td>\u0641\u0631\u0646\u0643 \u063a\u064a\u0646\u064a (\u0639)<\/td>\n<\/tr>\n<tr>\n<td>\u0639 ^ \u0646<\/td>\n<td>\u063a\u0641 (\u0639 ^ \u0646)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0648\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a<\/h2>\n<p>\u062a\u0644\u0639\u0628 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u062f\u0648\u0631\u064b\u0627 \u062d\u0627\u0633\u0645\u064b\u0627 \u0641\u064a \u0639\u0644\u0648\u0645 \u0648\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631\u060c \u062e\u0627\u0635\u0629 \u0641\u064a \u0646\u0642\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0628\u0631\u0648\u062a\u0648\u0643\u0648\u0644\u0627\u062a \u0627\u0644\u062a\u0634\u0641\u064a\u0631. \u0641\u0647\u064a \u0636\u0631\u0648\u0631\u064a\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u0634\u0641\u064a\u0631\u060c \u0645\u0645\u0627 \u064a\u0633\u0627\u0639\u062f \u0639\u0644\u0649 \u062a\u0635\u062d\u064a\u062d \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0641\u064a \u0646\u0642\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u0641\u064a \u0627\u0644\u062a\u0634\u0641\u064a\u0631\u060c \u0648\u062a\u0648\u0641\u064a\u0631 \u0627\u062a\u0635\u0627\u0644 \u0622\u0645\u0646 \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a.<\/p>\n<p>\u0623\u062d\u062f \u0627\u0644\u062a\u062d\u062f\u064a\u0627\u062a \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0641\u064a \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0647\u0648 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0627\u0644\u0630\u064a \u064a\u0646\u0637\u0648\u064a \u0639\u0644\u064a\u0647 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a. \u0648\u064a\u062a\u062c\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0628\u0634\u0643\u0644 \u062e\u0627\u0635 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0623\u0643\u0628\u0631. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u063a\u0627\u0644\u0628\u064b\u0627 \u0645\u0627 \u064a\u062a\u0645 \u062a\u062e\u0641\u064a\u0641 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062c\u062f\u0627\u0648\u0644 \u0627\u0644\u0628\u062d\u062b \u0623\u0648 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0633\u0631\u064a\u0639\u0629 \u0645\u062b\u0644 \u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0633\u0631\u064a\u0639 (FFT) \u0644\u0636\u0631\u0628 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f.<\/p>\n<h2>\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0642\u0627\u0631\u0646 \u0645\u0639 \u0645\u0641\u0627\u0647\u064a\u0645 \u0645\u0645\u0627\u062b\u0644\u0629<\/h2>\n<p>\u0645\u0642\u0627\u0631\u0646\u0629 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0628\u0645\u0641\u0627\u0647\u064a\u0645 \u0623\u062e\u0631\u0649 \u0645\u0645\u0627\u062b\u0644\u0629\u060c \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0648\u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0623\u0648 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a\u060c \u0648\u0647\u064a \u0647\u064a\u0627\u0643\u0644 \u062c\u0628\u0631\u064a\u0629 \u0623\u0643\u062b\u0631 \u0639\u0645\u0648\u0645\u064a\u0629.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0645\u0639\u0627\u0645\u0644<\/th>\n<th>\u0627\u0644\u0645\u062c\u0627\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f<\/th>\n<th>\u062c\u0631\u0633<\/th>\n<th>\u0645\u062c\u0645\u0648\u0639\u0629<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0625\u0646\u0647\u0627\u0621<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0644\u062a\u0631\u0627\u0628\u0637<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0647\u0648\u064a\u0629<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0639\u0643\u0648\u0633<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645 (\u0645\u0636\u0627\u0641)<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0644\u062a\u0628\u0627\u062f\u0644\u064a\u0629<\/td>\n<td>\u0646\u0639\u0645 (\u0643\u0644\u0627 \u0627\u0644\u0639\u0645\u0644\u064a\u062a\u064a\u0646)<\/td>\n<td>\u0646\u0639\u0645 (\u0625\u0636\u0627\u0641\u0629)<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a\u0629<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<td>\u0644\u0627<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0648\u062c\u0647\u0627\u062a \u0627\u0644\u0646\u0638\u0631 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629<\/h2>\n<p>\u0648\u0641\u064a \u0639\u0627\u0644\u0645 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u064a\u0629\u060c \u0645\u0646 \u0627\u0644\u0645\u062a\u0648\u0642\u0639 \u0623\u0646 \u062a\u0644\u0639\u0628 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u062f\u0648\u0631\u064b\u0627 \u0645\u0647\u0645\u064b\u0627. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u062a\u0639\u062f \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0643\u0645\u0648\u0645\u064a\u0629 \u0623\u062d\u062f \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0645\u0628\u0627\u062f\u0626 \u0627\u0644\u062d\u0642\u0648\u0644 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0636\u0631\u0648\u0631\u064a\u0629\u060c \u062e\u0627\u0635\u0629 \u0641\u064a \u062a\u0635\u062d\u064a\u062d \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u0643\u0645\u0648\u0645\u064a\u0629 \u0648\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0634\u0641\u064a\u0631.<\/p>\n<p>\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0645\u0639 \u0638\u0647\u0648\u0631 \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a \u0648\u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a\u060c \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u062c\u062f \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u062c\u062f\u064a\u062f\u0629\u060c \u0648\u062e\u0627\u0635\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 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\u0627\u0644\u0639\u0627\u0644\u0645.<\/p>","protected":false},"featured_media":477242,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477241","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"","faq_items":null},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/477241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":1,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/477241\/revisions"}],"predecessor-version":[{"id":505549,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/477241\/revisions\/505549"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media\/477242"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media?parent=477241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}