已知一种[tex=2.071x1.357]fKtHfy5PkM/VRAijZ52i8A==[/tex]循环码的全部码组为[tex=18.0x2.357]CeOWlpLvH8Qhk/RmfIvBHYkVEkPOY8MuFlzJuPaF9YRDXiumO8Aw9HMXJ3FztJm0XTzE9WAIMhp/rwMwn0zTjQRGhMGd/A9A19vIj15rSms1FDLaa5aKyX8sP3SLQ3hfvZbUz3wtAMuHcY7Uc5OTtg==[/tex]试求：该循环码的生成多项式[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]、典型生成矩阵[tex=0.786x1.0]LyvDGollVJ+xwurtsLcn0g==[/tex]和典型监督矩阵[tex=0.857x1.0]aPLFPHMGSKDwulHSwLWugg==[/tex];

2022-07-29

已知一种[tex=2.071x1.357]fKtHfy5PkM/VRAijZ52i8A==[/tex]循环码的全部码组为[tex=18.0x2.357]CeOWlpLvH8Qhk/RmfIvBHYkVEkPOY8MuFlzJuPaF9YRDXiumO8Aw9HMXJ3FztJm0XTzE9WAIMhp/rwMwn0zTjQRGhMGd/A9A19vIj15rSms1FDLaa5aKyX8sP3SLQ3hfvZbUz3wtAMuHcY7Uc5OTtg==[/tex]试求：该循环码的生成多项式[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]、典型生成矩阵[tex=0.786x1.0]LyvDGollVJ+xwurtsLcn0g==[/tex]和典型监督矩阵[tex=0.857x1.0]aPLFPHMGSKDwulHSwLWugg==[/tex];

答案：

已知[tex=7.429x1.214]MRkX76ZFQeN8appUZG8xA9/SqHsoR2eIO4p/SZYasUk=[/tex]。根据生成多项式[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]对应前面[tex=2.643x1.357]dJJY8ypkRUoaYSlogPPMLg==[/tex]位皆为 0 的码组----“0010111”, 可得[tex=7.929x1.5]5m6izDDFSAwXFIRIaiZTAXTY/EBPtDKDXRZ+7tNiLa8=[/tex]由[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]可得生成矩阵[tex=17.857x4.643]4Palgf0RQgVzWyr/h9ZzcB605HuLEuInCW8PrGXdAhLbuRyd2AzqfI/76++fz65pvvMZHWbTGWxa+fop7ktU0klirOW9LVxYpeI9iogRISn6rUC9+XzhFTbaojDWWwciGtJFpyrPqbxIXXe/9IKLxm213M0SwMQsxfX+YQ4YqlGBM4ePuod78DAAvrxTy5P6Bnc/ocPEr8dofdYXL+PO+x/1YNiIgdineSGhs7IAHC6gu1/0m3alFGQz4zW1eIfd[/tex]即[tex=31.286x3.5]30PSVIg0f/V7AoqA54aFx3PQV15/gZTms49+NmwJX9xzsv5a2CkvOxJr3uuCFso77vWik9EnzWK6/0cqwAfbSRiq00L3i8o0+tf0vwO/BJj99QNpztfDtj6OPgGrpPPz1yWERT6UGT40PDeKoMxd3miudg8gaJgNSSv7+1Zv4fQyX3Jsd1H26YZghCn7x5M7aBvn2ASXmIbicS4mZmFBhlKNIRY5txI5AItYKFZwiDykZvQCkHHq1uN7A85IU/n5zFL3DDYV921UvyL4vxrN5SGDJG+YxPDrSad1s7Ld5jErHdzErzN2bwqwQXKho684J4I5m251fmNlrt9cjLCTSLhfN7e0x4bMFCBnfIGpz91nk/A5rgZ9iAiKSJ274vZce1qJi2JFpXpwF6HhLk1TCg==[/tex]其中[tex=19.786x4.5]Ag30ceVI6RySe1mN6l8ov3AqLdkigHHeT1dn3Rc+p1vKhiGiJ0TdtGBPEwjAJJpHR27i2x+D9MfWpMorW/KHghIqCoWez3KZAIlXSTzDbUEVqEGtC7f5ThyXmcyFtWQs+N+Nc4eFZGmLJvn74/a1ufArLXAX0QDNyHWEAOv/BQM+lQuvquwnRv/clOBzZR1micGmd4WnqL/5fPkUhwdi9BPQMj9apbbdU99eWbRLeWl/GX2zqBscPVibx8wIcnPvj0ym5K+UHXZie2ww/+R7BA==[/tex]于是，典型监督矩阵[tex=16.714x4.5]vzcsxDY3HjTE0PJYUXp/SGLXsgN8mFvZUICRqL2tPzSmaGfK1WHd4hUloT3dSNVW8NHzT3T1sUOJFFCJRwmM3UQzohTWB5lFSqE/QsTSzr/B/hc3/XNhhPM0615q0Im2zYI9HQv7tWSP0ffS12xjG17/X0BJzRoA/skL5ZofcXg0eSZBszjSeRd+Q9NZflBm7rXWMepW3hq/Vt+17QAIqCrLkOMTzrzb3SyO6+ob2uzd/QfTxedx9ElPJKsdbLyx[/tex]

举一反三

内容

0
已知一个[tex=2.071x1.357]GEir28FA4/d0c9UgaWIuCg==[/tex] 循环码的全部码组为[img=668x198]17a38b1f3d0f58e.png[/img]试写出该循环码的生成多项式[tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]和生成矩阵[tex=2.286x1.357]pCptTr/y7P2l6DnvbxLDfKs7GcYb2a/2ZcqB0Nw/VCU=[/tex], 并将[tex=2.286x1.357]pCptTr/y7P2l6DnvbxLDfKs7GcYb2a/2ZcqB0Nw/VCU=[/tex] 化成典型阵。
1
已知[tex=2.071x1.357]GEir28FA4/d0c9UgaWIuCg==[/tex]循环码的生成多项式为[tex=6.643x1.5]Bre+i6lXDwBsmXjLBQVm94tJpC6LKjpDFYhU4eZTMUk=[/tex]试求该[tex=2.071x1.357]GEir28FA4/d0c9UgaWIuCg==[/tex]循环码的典型生成矩阵和典型监督矩阵;[br][/br]
2
已知[tex=2.071x1.357]fKtHfy5PkM/VRAijZ52i8A==[/tex] 循环码的生成矩阵为[tex=7.429x3.5]krqLcez/NatiMpfHupaHv/jBV+daUeIEAvV3HGP7/6NJt7XUAYPw293TN4CfM3zjQyjckZx/nkC6ZffesezmeOiosuySiPKQuLl2ckZaZ0k=[/tex]若输入信息码为 [tex=1.5x1.0]SYPwVg8E46efdwmIbbbt2Q==[/tex] ,试写出对应的循环码码组;[br][/br]
3
若已知一个 [tex=2.071x1.357]fKtHfy5PkM/VRAijZ52i8A==[/tex]循环码生成多项式为[tex=8.357x1.5]n4HJvClqbt1ZBeAWOj1DoBxhXMEF4M/jeyF+cIiDDGg=[/tex], 试求其生成矩阵。
4
[tex=2.071x1.357]fKtHfy5PkM/VRAijZ52i8A==[/tex]循环码的生成多项式为[tex=8.357x1.5]DB5kFYU1oPINp0gcSUrh0AZ5/H1xR1bPNzYhnJtsUsE=[/tex]当数据[tex=6.857x1.357]lGDR+sEpgMCuk1qCoVhb4zG6F/IO7r3mpOFr84AcPMauTSg4xCfeK/8qRFvwSbc0qXVF0EP9hKxQ7QPZ4b+RPw==[/tex] 时, 求系统循环码的码组[tex=1.071x1.143]4o7BOOkOHDYl51MA15caQQ==[/tex]