{"id":1917,"date":"2026-04-14T19:20:32","date_gmt":"2026-04-14T11:20:32","guid":{"rendered":"http:\/\/www.preluna.xyz\/?p=1917"},"modified":"2026-04-14T19:20:35","modified_gmt":"2026-04-14T11:20:35","slug":"%e6%95%b0%e6%8d%ae%e9%93%be%e8%b7%af%e5%b1%82%e5%b7%ae%e9%94%99%e6%8e%a7%e5%88%b6%e8%bf%99%e4%b8%80%e5%9d%97%ef%bc%8c%e6%9c%80%e9%80%82%e5%90%88%e8%bf%99%e6%a0%b7%e4%b8%b2%e8%b5%b7%e6%9d%a5","status":"publish","type":"post","link":"http:\/\/www.preluna.xyz\/index.php\/2026\/04\/14\/%e6%95%b0%e6%8d%ae%e9%93%be%e8%b7%af%e5%b1%82%e5%b7%ae%e9%94%99%e6%8e%a7%e5%88%b6%e8%bf%99%e4%b8%80%e5%9d%97%ef%bc%8c%e6%9c%80%e9%80%82%e5%90%88%e8%bf%99%e6%a0%b7%e4%b8%b2%e8%b5%b7%e6%9d%a5\/preluna\/text\/","title":{"rendered":"\u6570\u636e\u94fe\u8def\u5c42\u5dee\u9519\u63a7\u5236\u8fd9\u4e00\u5757\uff0c\u6700\u9002\u5408\u8fd9\u6837\u4e32\u8d77\u6765"},"content":{"rendered":"\n

\u8fd9\u4e00\u90e8\u5206\u5728 408 \u98ce\u683c\u91cc\uff0c\u6700\u597d\u4e0d\u8981\u628a\u201c\u5947\u5076\u6821\u9a8c\u3001CRC\u3001\u6d77\u660e\u7801\u201d\u770b\u6210\u4e09\u5757\u4e92\u4e0d\u76f8\u5e72\u7684\u96f6\u6563\u77e5\u8bc6\uff0c\u800c\u662f\u8981\u6293\u4f4f\u4e00\u6761\u4e3b\u7ebf\uff1a\u7801\u8ddd\u51b3\u5b9a\u68c0\u9519\/\u7ea0\u9519\u80fd\u529b\uff0c\u68c0\u9519\u7801\u8d1f\u8d23\u53d1\u73b0\u9519\u8bef\uff0c\u7ea0\u9519\u7801\u8d1f\u8d23\u5b9a\u4f4d\u5e76\u7ea0\u6b63\u9519\u8bef<\/strong>\u3002\u4ece\u8003\u7814\u505a\u9898\u89d2\u5ea6\u770b\uff0c\u901a\u5e38\u662f\u6309\u201c\u7801\u8ddd \u2192 \u5947\u5076\u6821\u9a8c \u2192 CRC \u2192 \u6d77\u660e\u7801\u201d\u8fd9\u4e00\u6761\u7ebf\u6765\u590d\u4e60\u6700\u987a\u3002\u6700\u6838\u5fc3\u7684\u4e09\u4e2a\u5173\u7cfb\u5f0f\u662f\uff1a\u82e5\u8981\u68c0\u6d4b e \u4f4d\u9519<\/strong>\uff0c\u5219\u6700\u5c0f\u7801\u8ddd d >= e + 1<\/code>\uff1b\u82e5\u8981\u7ea0\u6b63 t \u4f4d\u9519<\/strong>\uff0c\u5219\u6700\u5c0f\u7801\u8ddd d >= 2t + 1<\/code>\uff1b\u82e5\u65e2\u8981\u7ea0\u9519\u53c8\u8981\u68c0\u9519\uff0c\u5219\u5e38\u7528\u5173\u7cfb\u662f d >= e + t + 1<\/code>\uff08\u8fd9\u91cc\u7684 e<\/code> \u6307\u989d\u5916\u8fd8\u80fd\u68c0\u6d4b\u51fa\u7684\u9519\u4f4d\u6570\uff09\u3002\u8fd9\u4e9b\u5173\u7cfb\u672c\u8d28\u4e0a\u90fd\u662f\u56f4\u7ed5\u201c\u5408\u6cd5\u7801\u5b57\u4e4b\u95f4\u5fc5\u987b\u62c9\u5f00\u8db3\u591f\u8ddd\u79bb\u201d\u5c55\u5f00\u7684\u3002(course.buct.edu.cn<\/a>)<\/p>\n\n\n\n

\u4ece\u8fd9\u4e00\u70b9\u51fa\u53d1\uff0c\u4e09\u7c7b\u7f16\u7801\u7684\u533a\u522b\u5c31\u5f88\u6e05\u695a\u4e86\u3002\u5947\u5076\u6821\u9a8c\u7801\u3001CRC \u5c5e\u4e8e\u68c0\u9519\u7801<\/strong>\uff0c\u91cd\u70b9\u662f\u201c\u53d1\u73b0\u9519\u4e86\u6ca1\u6709\u201d\uff1b\u6d77\u660e\u7801\u5c5e\u4e8e\u7ea0\u9519\u7801<\/strong>\uff0c\u91cd\u70b9\u662f\u201c\u53d1\u73b0\u540e\u8fd8\u80fd\u4e0d\u80fd\u5b9a\u4f4d\u5e76\u6539\u6b63\u201d\u3002\u56e0\u6b64\uff0c\u201c\u6570\u636e\u94fe\u8def\u5c42\u53ea\u80fd\u5dee\u9519\u68c0\u6d4b\uff0c\u4e0d\u80fd\u5dee\u9519\u7ea0\u6b63\u201d\u8fd9\u79cd\u8bf4\u6cd5\u5982\u679c\u6309\u7edd\u5bf9\u5316\u8868\u8ff0\u6765\u5224\u65ad\uff0c\u662f\u9519<\/strong>\u7684\u3002\u66f4\u51c6\u786e\u7684\u8bf4\u6cd5\u662f\uff1a\u6570\u636e\u94fe\u8def\u5c42\u7684\u5dee\u9519\u63a7\u5236\u65e2\u5305\u62ec\u68c0\u9519\u4e5f\u5305\u62ec\u7ea0\u9519\uff1b\u53ea\u662f\u8ba1\u7b97\u673a\u7f51\u7edc\u6559\u6750\u548c\u5b9e\u9645\u534f\u8bae\u91cc\uff0c\u66f4\u5e38\u89c1\u7684\u662f CRC \u68c0\u9519 + \u91cd\u4f20<\/strong>\uff0c\u800c\u4e0d\u662f\u628a\u6d77\u660e\u7801\u4f5c\u4e3a\u4e3b\u6d41\u94fe\u8def\u5c42\u534f\u8bae\u7684\u6838\u5fc3\u673a\u5236\u3002(CSDN\u535a\u5ba2<\/a>)<\/p>\n\n\n\n

\u5947\u5076\u6821\u9a8c\u7801\u4e3a\u4ec0\u4e48\u603b\u7231\u8003\u201c1 \u4f4d\u9519\u201d\u548c\u201c\u5947\u6570\u4f4d\u9519\u201d<\/h2>\n\n\n\n

\u5947\u5076\u6821\u9a8c\u7801\u6700\u7b80\u5355\uff0c\u53ea\u52a0 1 \u4f4d\u6821\u9a8c\u4f4d<\/strong>\u3002\u82e5\u91c7\u7528\u5076\u6821\u9a8c\uff0c\u5c31\u8ba9\u201c\u6570\u636e\u4f4d + \u6821\u9a8c\u4f4d\u201d\u4e2d 1 \u7684\u603b\u4e2a\u6570\u4e3a\u5076\u6570\uff1b\u82e5\u91c7\u7528\u5947\u6821\u9a8c\uff0c\u5c31\u8ba9\u603b\u4e2a\u6570\u4e3a\u5947\u6570\u3002\u5b83\u7684\u672c\u8d28\u4e0d\u662f\u201c\u770b\u54ea\u4e00\u4f4d\u9519\u4e86\u201d\uff0c\u800c\u53ea\u662f\u201c\u770b\u6574\u4f53\u5947\u5076\u6027\u6709\u6ca1\u6709\u53d8\u5316\u201d\u3002(\u534e\u4e3a\u4e91\u793e\u533a<\/a>)<\/p>\n\n\n\n

\u4e5f\u6b63\u56e0\u4e3a\u5982\u6b64\uff0c\u5947\u5076\u6821\u9a8c\u7801\u6709\u4e24\u4e2a\u975e\u5e38\u9ad8\u9891\u7684\u7ed3\u8bba\u3002<\/p>\n\n\n\n

\u7b2c\u4e00\uff0c\u4e00\u5b9a\u80fd\u68c0\u51fa 1 \u4f4d\u9519\u8bef<\/strong>\u3002\u56e0\u4e3a\u53ea\u8981\u6709 1 \u4f4d\u7ffb\u8f6c\uff0c1 \u7684\u603b\u4e2a\u6570\u5947\u5076\u6027\u4e00\u5b9a\u6539\u53d8\uff0c\u6240\u4ee5\u7acb\u523b\u80fd\u53d1\u73b0\u3002<\/p>\n\n\n\n

\u7b2c\u4e8c\uff0c\u51e1\u662f\u5947\u6570\u4f4d\u9519\u8bef\u90fd\u80fd\u68c0\u51fa<\/strong>\u3002\u539f\u56e0\u548c\u4e0a\u9762\u5b8c\u5168\u4e00\u6837\uff1a\u6bcf\u7ffb\u8f6c 1 \u4f4d\uff0c\u5947\u5076\u6027\u5c31\u53d8\u4e00\u6b21\uff1b\u7ffb\u8f6c\u5947\u6570\u6b21\uff0c\u6700\u7ec8\u5947\u5076\u6027\u4e00\u5b9a\u6539\u53d8\uff0c\u6240\u4ee5\u80fd\u53d1\u73b0\u3002\u53cd\u8fc7\u6765\uff0c\u5076\u6570\u4f4d\u9519\u8bef\u4e0d\u4e00\u5b9a\u80fd\u68c0\u51fa<\/strong>\uff0c\u56e0\u4e3a\u7ffb\u8f6c\u5076\u6570\u6b21\u4ee5\u540e\uff0c\u6574\u4f53\u5947\u5076\u6027\u53ef\u80fd\u53c8\u56de\u5230\u4e86\u539f\u6765\u7684\u72b6\u6001\u3002(\u534e\u4e3a\u4e91\u793e\u533a<\/a>)<\/p>\n\n\n\n

\u8fd9\u4e00\u5757\u6700\u5bb9\u6613\u9519\u7684\u5730\u65b9\u5c31\u5728\u4e8e\uff0c\u5f88\u591a\u9898\u76ee\u628a\u201c\u80fd\u68c0 1 \u4f4d\u9519\u201d\u6545\u610f\u8bf4\u6210\u201c\u53ea\u80fd\u68c0 1 \u4f4d\u9519\u201d\u3002\u8fd9\u662f\u9519\u7684\u3002\u5947\u5076\u6821\u9a8c\u5e76\u4e0d\u662f\u53ea\u80fd\u53d1\u73b0 1 \u4f4d\u9519\uff0c\u800c\u662f\u80fd\u53d1\u73b0\u6240\u6709\u5947\u6570\u4f4d\u9519\uff0c\u4e0d\u80fd\u4fdd\u8bc1\u53d1\u73b0\u5076\u6570\u4f4d\u9519<\/strong>\u3002\u6240\u4ee5\u8003\u8bd5\u91cc\u770b\u5230\u201c\u5947\u5076\u6821\u9a8c\u53ef\u68c0\u5947\u6570\u4f4d\u9519\u201d\u8981\u7acb\u523b\u53cd\u5e94\u8fc7\u6765\uff1a\u8fd9\u53e5\u8bdd\u662f\u5bf9\u7684\uff1b\u770b\u5230\u201c\u5947\u5076\u6821\u9a8c\u53ef\u68c0\u4efb\u610f 2 \u4f4d\u9519\u201d\u5c31\u8981\u7acb\u523b\u5224\u9519\u3002<\/p>\n\n\n\n

CRC \u4e3a\u4ec0\u4e48\u662f\u68c0\u9519\u9898\u7684\u91cd\u5934\u620f<\/h2>\n\n\n\n

CRC \u662f 408 \u91cc\u6700\u91cd\u8981\u7684\u68c0\u9519\u7f16\u7801\u3002\u5b83\u4e0d\u662f\u9760\u201c\u6570 1 \u7684\u4e2a\u6570\u201d\uff0c\u800c\u662f\u628a\u4e8c\u8fdb\u5236\u5e8f\u5217\u5f53\u4f5c\u591a\u9879\u5f0f\uff0c\u7528\u751f\u6210\u591a\u9879\u5f0f\u53bb\u505a \u6a21 2 \u9664\u6cd5<\/strong>\u3002\u9898\u76ee\u901a\u5e38\u8003\u56db\u4ef6\u4e8b\uff1a<\/p>\n\n\n\n

\u7b2c\u4e00\uff0c\u5df2\u77e5\u6570\u636e\u548c\u751f\u6210\u591a\u9879\u5f0f\uff0c\u6c42 CRC \u6821\u9a8c\u7801\u3002
\u7b2c\u4e8c\uff0c\u5df2\u77e5\u53d1\u9001\u7801\u5b57\u548c\u751f\u6210\u591a\u9879\u5f0f\uff0c\u5224\u65ad\u6709\u6ca1\u6709\u51fa\u9519\u3002
\u7b2c\u4e09\uff0c\u5df2\u77e5\u63a5\u6536\u5e8f\u5217\uff0c\u53cd\u63a8\u539f\u6570\u636e\u548c CRC \u4f4d\u3002
\u7b2c\u56db\uff0c\u8fa8\u6790\u201c\u4f59\u6570\u4e3a 0\u201d\u5230\u5e95\u8868\u793a\u4ec0\u4e48\u3002<\/p>\n\n\n\n

CRC \u7684\u6807\u51c6\u505a\u6cd5\u56fa\u5b9a\u4e0d\u53d8\uff1a<\/p>\n\n\n\n

\u8bbe\u539f\u59cb\u6570\u636e\u4e3a M<\/code>\uff0c\u751f\u6210\u591a\u9879\u5f0f\u4e3a G(x)<\/code>\uff0c\u5176\u6700\u9ad8\u6b21\u5e42\u4e3a r<\/code>\u3002
\u5148\u5728 M<\/code> \u540e\u8865 r<\/code> \u4e2a 0\uff0c\u5f97\u5230 M\u00b72^r<\/code>\u3002
\u518d\u7528\u5b83\u53bb\u9664\u4ee5\u5bf9\u5e94\u7684\u751f\u6210\u591a\u9879\u5f0f\u4e8c\u8fdb\u5236\u4e32\uff0c\u5f97\u5230\u4f59\u6570 R<\/code>\u3002
\u6700\u540e\u53d1\u9001\u7801\u5b57\u5c31\u662f T = M || R<\/code>\u3002
\u63a5\u6536\u7aef\u62ff\u6536\u5230\u7684\u5e8f\u5217\u518d\u53bb\u9664\u4ee5\u751f\u6210\u591a\u9879\u5f0f\uff0c\u5982\u679c\u4f59\u6570\u4e3a 0\uff0c\u5c31\u8bf4\u660e\u672a\u68c0\u6d4b\u5230\u5dee\u9519<\/strong>\u3002\u6ce8\u610f\uff0c\u8fd9\u91cc\u53ea\u80fd\u8bf4\u201c\u672a\u68c0\u6d4b\u5230\u5dee\u9519\u201d\uff0c\u4e0d\u80fd\u7edd\u5bf9\u8bf4\u201c\u4f20\u8f93\u4e00\u5b9a\u5b8c\u5168\u6b63\u786e\u201d\u3002(\u535a\u5ba2\u56ed<\/a>)<\/p>\n\n\n\n

\u8fd9\u91cc\u6700\u5bb9\u6613\u9519\u7684\u70b9\u6709\u4e24\u4e2a\u3002\u4e00\u4e2a\u662f\u628a\u666e\u901a\u51cf\u6cd5\u5f53\u6210 CRC \u9664\u6cd5\uff0c\u5b9e\u9645\u4e0a CRC \u7528\u7684\u662f\u6a21 2 \u9664\u6cd5<\/strong>\uff0c\u4e5f\u5c31\u662f\u201c\u540c 0 \u5f02 1\u201d\uff0c\u672c\u8d28\u662f\u5f02\u6216\u3002\u53e6\u4e00\u4e2a\u662f\u628a\u201c\u4f59\u6570\u4e3a 0\u201d\u7406\u89e3\u6210\u201c\u7edd\u5bf9\u6ca1\u9519\u201d\uff0c\u8fd9\u4e5f\u4e0d\u4e25\u8c28\u3002CRC \u53ea\u662f\u68c0\u9519\u80fd\u529b\u5f88\u5f3a<\/strong>\uff0c\u4e0d\u662f\u6570\u5b66\u4e0a\u7edd\u5bf9\u4e0d\u4f1a\u6f0f\u68c0\u3002<\/p>\n\n\n\n

\u6d77\u660e\u7801\u4e3a\u4ec0\u4e48\u5c5e\u4e8e\u7ea0\u9519\u7f16\u7801<\/h2>\n\n\n\n

\u6d77\u660e\u7801\u548c\u524d\u9762\u7684\u68c0\u9519\u7801\u4e0d\u4e00\u6837\uff0c\u5b83\u7684\u91cd\u70b9\u5df2\u7ecf\u4e0d\u662f\u201c\u6709\u6ca1\u6709\u9519\u201d\uff0c\u800c\u662f\u201c\u9519\u5728\u54ea\u4e00\u4f4d\u201d\u3002\u5b83\u901a\u8fc7\u5728\u82e5\u5e72\u7279\u6b8a\u4f4d\u7f6e\u63d2\u5165\u6821\u9a8c\u4f4d\uff0c\u8ba9\u6bcf\u4e00\u4e2a\u6570\u636e\u4f4d\u90fd\u843d\u5728\u4e00\u7ec4\u72ec\u7279\u7684\u6821\u9a8c\u5173\u7cfb\u4e2d\u3002\u63a5\u6536\u7aef\u91cd\u65b0\u8ba1\u7b97\u8fd9\u4e9b\u6821\u9a8c\u5173\u7cfb\u540e\uff0c\u4f1a\u5f97\u5230\u4e00\u4e2a\u201c\u7efc\u5408\u6821\u9a8c\u7ed3\u679c\u201d\uff0c\u4e5f\u5c31\u662f\u5e38\u8bf4\u7684\u6821\u9a8c\u5b50<\/strong>\u6216\u7efc\u5408\u75c7<\/strong>\uff0c\u8fd9\u4e2a\u7ed3\u679c\u53ef\u4ee5\u76f4\u63a5\u6307\u51fa\u54ea\u4e00\u4f4d\u51fa\u9519\u3002(\u897f\u5b89\u4ea4\u901a\u5927\u5b66<\/a>)<\/p>\n\n\n\n

\u8003\u7814\u91cc\u6700\u5e38\u7528\u7684\u6d77\u660e\u7801\u7ed3\u8bba\u6709\u4e24\u4e2a\u3002<\/p>\n\n\n\n

\u4e00\u4e2a\u662f\u6821\u9a8c\u4f4d\u4e2a\u6570\u516c\u5f0f<\/strong>\u3002\u82e5\u4fe1\u606f\u4f4d\u6709 m<\/code> \u4f4d\uff0c\u6821\u9a8c\u4f4d\u6709 r<\/code> \u4f4d\uff0c\u5219\u5e94\u6ee1\u8db3\uff1a<\/p>\n\n\n\n

2^r >= m + r + 1<\/code><\/p>\n\n\n\n

\u8fd9\u6761\u5f0f\u5b50\u4e00\u5b9a\u8981\u4f1a\u7528\uff0c\u56e0\u4e3a\u201c\u7ed9\u5b9a\u6570\u636e\u4f4d\u6570\uff0c\u6c42\u81f3\u5c11\u52a0\u591a\u5c11\u4f4d\u6821\u9a8c\u4f4d\u201d\u662f\u6d77\u660e\u7801\u6700\u5e38\u89c1\u7684\u8ba1\u7b97\u9898\u3002(\u897f\u5b89\u4ea4\u901a\u5927\u5b66<\/a>)<\/p>\n\n\n\n

\u53e6\u4e00\u4e2a\u662f\u6d77\u660e\u7801\u548c\u7801\u8ddd\u7684\u5173\u7cfb\u3002\u6807\u51c6\u6d77\u660e\u7801\u5e38\u6309\u201c\u7ea0\u6b63 1 \u4f4d\u9519<\/strong>\u201d\u6765\u7406\u89e3\uff1b\u4ece\u6700\u5c0f\u7801\u8ddd\u89d2\u5ea6\u770b\uff0c\u5b83\u5bf9\u5e94\u7684\u662f\u6700\u5c0f\u7801\u8ddd\u4e3a 3 \u7684\u601d\u8def\uff0c\u6240\u4ee5\u5b83\u4e0e\u201c\u5355\u9519\u7ea0\u6b63\u201d\u7d27\u5bc6\u76f8\u5173\u3002\u56fd\u5185\u8003\u8bd5\u8bed\u5883\u91cc\uff0c\u901a\u5e38\u76f4\u63a5\u8bb0\u6210\u201c\u6d77\u660e\u7801\u80fd\u7ea0 1 \u4f4d\u9519\u201d\u3002(ci.tongji.edu.cn<\/a>)<\/p>\n\n\n\n

\u4f8b\u9898 1\uff1a\u201c\u6570\u636e\u94fe\u8def\u5c42\u53ea\u80fd\u63d0\u4f9b\u5dee\u9519\uff0c\u800c\u4e0d\u80fd\u63d0\u4f9b\u5dee\u9519\u7ea0\u6b63\u201d\u5bf9\u8fd8\u662f\u9519<\/h2>\n\n\n\n

\u8fd9\u53e5\u8bdd\u6309\u8003\u7814\u5224\u65ad\u5e94\u4e3a\uff1a\u9519<\/strong>\u3002<\/p>\n\n\n\n

\u539f\u56e0\u4e0d\u662f\u5f88\u590d\u6742\u3002\u6570\u636e\u94fe\u8def\u5c42\u7684\u201c\u5dee\u9519\u63a7\u5236\u201d\u672c\u6765\u5c31\u5305\u62ec\u4e24\u90e8\u5206\uff1a\u68c0\u9519<\/strong>\u548c\u7ea0\u9519<\/strong>\u3002CRC\u3001\u5947\u5076\u6821\u9a8c\u7801\u5c5e\u4e8e\u68c0\u9519\uff0c\u6d77\u660e\u7801\u5c5e\u4e8e\u7ea0\u9519\u3002\u53ea\u662f\u4ece\u8ba1\u7b97\u673a\u7f51\u7edc\u534f\u8bae\u7684\u4e3b\u6d41\u505a\u6cd5\u6765\u770b\uff0c\u94fe\u8def\u5c42\u66f4\u5e38\u89c1\u7684\u662f\u201c\u53d1\u73b0\u51fa\u9519\u4ee5\u540e\u91cd\u4f20\u201d\uff0c\u800c\u4e0d\u662f\u50cf\u4fe1\u9053\u7f16\u7801\u90a3\u6837\u5927\u91cf\u91c7\u7528\u524d\u5411\u7ea0\u9519\u3002\u6240\u4ee5\u6559\u6750\u91cc\u5e38\u7ed9\u4eba\u4e00\u79cd\u201c\u94fe\u8def\u5c42\u4e3b\u8981\u505a\u68c0\u9519\u201d\u7684\u5370\u8c61\uff0c\u4f46\u4e0d\u80fd\u76f4\u63a5\u8bf4\u201c\u94fe\u8def\u5c42\u4e0d\u80fd\u7ea0\u9519\u201d\u3002(CSDN\u535a\u5ba2<\/a>)<\/p>\n\n\n\n

\u8fd9\u7c7b\u5224\u65ad\u9898\u7684\u9677\u9631\u5c31\u5728\u201c\u53ea\u80fd\u201d\u4e8c\u5b57\u3002\u53ea\u8981\u9898\u5e72\u7528\u4e86\u7edd\u5bf9\u5316\u8868\u8ff0\uff0c\u5c31\u8981\u63d0\u9ad8\u8b66\u60d5\u3002<\/p>\n\n\n\n

\u4f8b\u9898 2\uff1a\u7ea0\u6b63 2 \u6bd4\u7279\u9519\u8bef\uff0c\u7801\u8ddd\u81f3\u5c11\u662f\u591a\u5c11<\/h2>\n\n\n\n

\u8bbe\u8981\u7ea0\u6b63 t = 2<\/code> \u4f4d\u9519\u8bef\u3002\u6839\u636e\u7ea0\u9519\u80fd\u529b\u516c\u5f0f\uff1a<\/p>\n\n\n\n

d >= 2t + 1<\/code><\/p>\n\n\n\n

\u6240\u4ee5\uff1a<\/p>\n\n\n\n

d >= 2\u00d72 + 1 = 5<\/code><\/p>\n\n\n\n

\u56e0\u6b64\u7b54\u6848\u662f\uff1a\u6700\u5c0f\u7801\u8ddd\u81f3\u5c11\u4e3a 5<\/strong>\u3002(course.buct.edu.cn<\/a>)<\/p>\n\n\n\n

\u8fd9\u9898\u975e\u5e38\u57fa\u7840\uff0c\u4f46\u5f88\u5bb9\u6613\u548c\u201c\u68c0\u6d4b e \u4f4d\u9519\u9700\u8981 d >= e + 1<\/code>\u201d\u6df7\u6389\u3002\u770b\u5230\u201c\u7ea0\u6b63\u201d\u4e8c\u5b57\uff0c\u8111\u5b50\u91cc\u5fc5\u987b\u7acb\u523b\u5207\u5230 2t + 1<\/code>\u3002<\/p>\n\n\n\n

\u4f8b\u9898 3\uff1a10 \u4f4d\u6570\u636e\u91c7\u7528\u6d77\u660e\u7801\uff0c\u9700\u8981\u589e\u52a0\u591a\u5c11\u4f4d\u5197\u4f59\u4f4d<\/h2>\n\n\n\n

\u8bbe\u6570\u636e\u4f4d m = 10<\/code>\uff0c\u6821\u9a8c\u4f4d r<\/code> \u6ee1\u8db3\uff1a<\/p>\n\n\n\n

2^r >= m + r + 1<\/code><\/p>\n\n\n\n

\u4ee3\u5165\u53ef\u5f97\uff1a<\/p>\n\n\n\n

\u5f53 r = 3<\/code> \u65f6\uff0c2^3 = 8 < 10 + 3 + 1 = 14<\/code>\uff0c\u4e0d\u6ee1\u8db3\u3002
\u5f53 r = 4<\/code> \u65f6\uff0c2^4 = 16 >= 10 + 4 + 1 = 15<\/code>\uff0c\u6ee1\u8db3\u3002<\/p>\n\n\n\n

\u6240\u4ee5\u81f3\u5c11\u9700\u8981\u589e\u52a0 4 \u4f4d\u5197\u4f59\u4fe1\u606f\u4f4d<\/strong>\u3002(\u897f\u5b89\u4ea4\u901a\u5927\u5b66<\/a>)<\/p>\n\n\n\n

\u8fd9\u7c7b\u9898\u5c31\u662f\u7eaf\u4ee3\u516c\u5f0f\uff0c\u51e0\u4e4e\u6ca1\u6709\u6280\u5de7\uff0c\u5173\u952e\u662f\u522b\u628a\u4e0d\u7b49\u5f0f\u5199\u9519\u3002<\/p>\n\n\n\n

\u4f8b\u9898 4\uff1a\u67d0\u5dee\u9519\u7f16\u7801\u7684\u7f16\u7801\u96c6\u4e3a {10011010, 01011100, 11110000, 00001111}\uff0c\u5176\u68c0\u6d4b\u548c\u7ea0\u9519\u80fd\u529b\u662f\u591a\u5c11<\/h2>\n\n\n\n

\u4f60\u8fd9\u9053\u9898\u539f\u6587\u91cc\u6709\u4e9b\u5206\u9694\u7b26\u660e\u663e\u88ab\u8bc6\u522b\u4e71\u4e86\uff0c\u6309\u6700\u5e38\u89c1\u9898\u578b\uff0c\u5e94\u7406\u89e3\u4e3a\u8fd9 4 \u4e2a 8 \u4f4d\u7801\u5b57\u6784\u6210\u4e00\u4e2a\u7f16\u7801\u96c6\u3002\u505a\u6cd5\u662f\u5148\u6c42\u6700\u5c0f\u7801\u8ddd<\/strong>\u3002<\/p>\n\n\n\n

\u4e24\u4e24\u6bd4\u8f83\u53ef\u5f97\uff1a<\/p>\n\n\n\n

d(10011010,01011100)=4<\/code>
d(10011010,11110000)=4<\/code>
d(10011010,00001111)=4<\/code>
d(01011100,11110000)=4<\/code>
d(01011100,00001111)=4<\/code>
d(11110000,00001111)=8<\/code><\/p>\n\n\n\n

\u6240\u4ee5\u6700\u5c0f\u7801\u8ddd d = 4<\/code>\u3002<\/p>\n\n\n\n

\u4e8e\u662f\uff1a<\/p>\n\n\n\n

\u82e5\u53ea\u8c08\u68c0\u9519\u80fd\u529b\uff0c\u5219\u53ef\u68c0 d - 1 = 3<\/code> \u4f4d\u9519\u3002
\u82e5\u53ea\u8c08\u7ea0\u9519\u80fd\u529b\uff0c\u5219\u53ef\u7ea0 floor((d - 1)\/2) = 1<\/code> \u4f4d\u9519\u3002
\u82e5\u9898\u76ee\u8981\u6c42\u201c\u540c\u65f6\u5177\u6709\u7684\u68c0\u9519\u548c\u7ea0\u9519\u80fd\u529b\u201d\uff0c\u5219\u6ee1\u8db3 d >= e + t + 1<\/code>\u3002\u4ee3\u5165 d = 4<\/code>\uff0c\u53ef\u5f97\u4e00\u79cd\u6807\u51c6\u8868\u8ff0\u662f\uff1a\u7ea0\u6b63 1 \u4f4d\u9519\uff0c\u540c\u65f6\u68c0\u6d4b 2 \u4f4d\u9519<\/strong>\u3002(course.buct.edu.cn<\/a>)<\/p>\n\n\n\n

\u8fd9\u7c7b\u9898\u6700\u5bb9\u6613\u9519\u5728\u6700\u540e\u4e00\u53e5\u3002\u5f88\u591a\u540c\u5b66\u7b97\u51fa d=4<\/code> \u540e\uff0c\u53ea\u4f1a\u7b54\u201c\u68c0 3 \u7ea0 1\u201d\uff0c\u5176\u5b9e\u8fd9\u4e24\u4e2a\u8bf4\u6cd5\u5206\u522b\u5bf9\u5e94\u201c\u53ea\u68c0\u9519\u6a21\u5f0f\u201d\u548c\u201c\u53ea\u7ea0\u9519\u6a21\u5f0f\u201d\u3002\u82e5\u9898\u5e72\u5f3a\u8c03\u201c\u68c0\u6d4b\u548c\u7ea0\u9519\u80fd\u529b\u201d\uff0c\u6700\u597d\u628a\u4e09\u79cd\u8bf4\u6cd5\u90fd\u4ea4\u4ee3\u6e05\u695a\uff0c\u6700\u7a33\u3002<\/p>\n\n\n\n

\u4f8b\u9898 5\uff1a\u6536\u5230\u6bd4\u7279\u5e8f\u5217 10110011010\uff0c\u751f\u6210\u591a\u9879\u5f0f\u4e3a G(x)=x\u2074+x\u00b3+1\uff0c\u5224\u65ad\u662f\u5426\u51fa\u9519\uff1b\u82e5\u672a\u51fa\u9519\uff0c\u6c42\u539f\u6570\u636e\u548c CRC \u7801<\/h2>\n\n\n\n

\u4f60\u9898\u76ee\u91cc\u5199\u6210\u4e86 G(x)=x+x+1<\/code>\uff0c\u8fd9\u5728 CRC \u9898\u91cc\u663e\u7136\u4e0d\u6210\u7acb\u3002\u7ed3\u5408\u8fd9\u9053\u9898\u7684\u5e38\u89c1\u539f\u9898\uff0c\u5e94\u5f53\u662f\uff1a<\/p>\n\n\n\n

G(x) = x^4 + x^3 + 1<\/code><\/p>\n\n\n\n

\u5bf9\u5e94\u4e8c\u8fdb\u5236\u9664\u6570\u4e3a 11001<\/strong>\u3002\u8fd9\u4e2a\u9898\u578b\u672c\u8eab\u5728\u5e38\u89c1\u9898\u5e93\u91cc\u5c31\u662f\u8fd9\u6837\u51fa\u7684\u3002(\u725b\u5ba2\u7f51<\/a>)<\/p>\n\n\n\n

\u5148\u9a8c\u8bc1\u6536\u5230\u7684\u5e8f\u5217 10110011010<\/code> \u662f\u5426\u51fa\u9519\u3002
\u505a\u6a21 2 \u9664\u6cd5\uff1a<\/p>\n\n\n\n

10110011010 \u00f7 11001<\/code><\/p>\n\n\n\n

\u6309\u5f02\u6216\u9664\u6cd5\u7ee7\u7eed\u505a\u4e0b\u53bb\uff0c\u6700\u540e\u4f59\u6570\u4e3a\uff1a<\/p>\n\n\n\n

0000<\/code><\/p>\n\n\n\n

\u6240\u4ee5\u7ed3\u8bba\u662f\uff1a\u672a\u68c0\u6d4b\u5230\u5dee\u9519<\/strong>\u3002(\u725b\u5ba2\u7f51<\/a>)<\/p>\n\n\n\n

\u65e2\u7136\u751f\u6210\u591a\u9879\u5f0f\u6700\u9ad8\u6b21\u5e42\u662f 4\uff0c\u90a3\u4e48 CRC \u6821\u9a8c\u4f4d\u957f\u5ea6\u5c31\u662f 4 \u4f4d\u3002\u56e0\u6b64\u6536\u5230\u7684 11 \u4f4d\u7801\u5b57\u53ef\u4ee5\u62c6\u6210\uff1a<\/p>\n\n\n\n

\u539f\u59cb\u6570\u636e\uff1a\u524d 7 \u4f4d 1011001<\/code>
CRC \u6821\u9a8c\u7801\uff1a\u540e 4 \u4f4d 1010<\/code><\/p>\n\n\n\n

\u8fd8\u53ef\u4ee5\u53cd\u5411\u9a8c\u8bc1\u4e00\u6b21\uff1a
\u628a\u539f\u6570\u636e 1011001<\/code> \u540e\u8865 4 \u4e2a 0\uff0c\u5f97\u5230 10110010000<\/code>\uff1b
\u518d\u7528 11001<\/code> \u53bb\u9664\uff0c\u4f59\u6570\u6070\u597d\u4e3a 1010<\/code>\uff1b
\u56e0\u6b64\u53d1\u9001\u7801\u5b57\u5c31\u662f\uff1a<\/p>\n\n\n\n

1011001 || 1010 = 10110011010<\/code><\/p>\n\n\n\n

\u4e0e\u63a5\u6536\u5e8f\u5217\u4e00\u81f4\uff0c\u6240\u4ee5\u7b54\u6848\u6210\u7acb\u3002(\u725b\u5ba2\u7f51<\/a>)<\/p>\n\n\n\n

\u6700\u540e\u628a\u8fd9\u4e00\u7ae0\u538b\u6210\u4e00\u4e2a\u505a\u9898\u6a21\u677f<\/h2>\n\n\n\n

\u8fd9\u4e00\u7ae0\u6700\u9002\u5408\u8bb0\u6210\u4e0b\u9762\u8fd9\u5957\u5224\u65ad\u987a\u5e8f\u3002<\/p>\n\n\n\n

\u5148\u770b\u9898\u76ee\u662f\u5728\u95ee\u68c0\u9519<\/strong>\u8fd8\u662f\u7ea0\u9519<\/strong>\u3002
\u5982\u679c\u662f\u5947\u5076\u6821\u9a8c\uff0c\u7acb\u523b\u60f3\u5230\uff1a\u68c0 1 \u4f4d\u6ca1\u95ee\u9898\uff0c\u68c0\u4efb\u610f\u5947\u6570\u4f4d\u6ca1\u95ee\u9898\uff0c\u5076\u6570\u4f4d\u4e0d\u4fdd\u8bc1<\/strong>\u3002(\u534e\u4e3a\u4e91\u793e\u533a<\/a>)
\u5982\u679c\u662f CRC\uff0c\u7acb\u523b\u60f3\u5230\uff1a\u8865\u96f6\u3001\u6a21 2 \u9664\u3001\u53d6\u4f59\u6570\u3001\u62fc\u63a5\u7801\u5b57\u3001\u63a5\u6536\u7aef\u518d\u9664<\/strong>\u3002(\u535a\u5ba2\u56ed<\/a>)
\u5982\u679c\u662f\u6d77\u660e\u7801\uff0c\u7acb\u523b\u60f3\u5230\uff1a\u5148\u7b97\u6821\u9a8c\u4f4d\u4e2a\u6570 2^r >= m + r + 1<\/code><\/strong>\u3002(\u897f\u5b89\u4ea4\u901a\u5927\u5b66<\/a>)
\u5982\u679c\u9898\u76ee\u7ed9\u4e86\u4e00\u7ec4\u7801\u5b57\uff0c\u7acb\u523b\u60f3\u5230\uff1a\u5148\u6c42\u6700\u5c0f\u7801\u8ddd\uff0c\u518d\u5957 \u68c0\u9519 d-1\uff0c\u7ea0\u9519 floor((d-1)\/2)<\/code><\/strong>\u3002(course.buct.edu.cn<\/a>)<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

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