??a6???a??1001110?5??0??0100111???a4???1100010?????a?3???0?
?0110001???0???a2??a???0???1??a0??由矩阵的初等变换可得典型监督矩阵
??1011000?H??1110100???1100010?? ?0110001??根据监督矩阵和生成矩阵的关系可得生成矩阵为：
?1001110?G???0100111? ?0011101????12-7 已知（15,5）循环码的生成多项式为g(x)?x10?x8?x5?x4?x?1，（1）试求该码的生成矩阵；
（2）写出信息码为 m(x)?x4?x?1 时的码多项式。 解：（1）由生成多项式可得生成矩阵为：
??x14?x12?x9?x8?x5?x4??x13?x11?x8?x7?x4?x3?G(x)???x12?x10?x7??x6?x3?x2?
?x11?x9?x6?x5?x2?x????x10?x8?x5?x4?x?1????101001100110000?010100110011000?G????001010011001100??
?000101001100110????000010100110011??(2)由信息码多项式得信息码元为m=（10011）,mG=A
??101001100110000?010100110011000??10011?????001010011001100???000101001100110????000010100110011???101110001100101? 由码组可得码多项式为：
T(x)?x14?x12?x11?x10?x6?x5?x2?1
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