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<p class=MsoNormal><b><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>解：</span></b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>同上利用：</span><span
lang=EN-US><span style='mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1105" type="#_x0000_t75" style='width:103.2pt;height:18pt' o:ole="">
<v:imagedata src="./ex5.files/image059.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=138 height=24
src="./ex5.files/image065.gif" v:shapes="_x0000_i1105"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1105"
DrawAspect="Content" ObjectID="_1069593295">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=MsoNormal><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>在本题中，</span><span lang=EN-US><span
style='mso-text-raise:-4.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1117"
type="#_x0000_t75" style='width:55.2pt;height:15pt' o:ole="">
<v:imagedata src="./ex5.files/image066.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=74 height=20
src="./ex5.files/image067.gif" v:shapes="_x0000_i1117"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1117"
DrawAspect="Content" ObjectID="_1069593296">
</o:OLEObject>
</xml><![endif]--></span><span style='font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，所以</span><span
lang=EN-US><span style='mso-text-raise:-60.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1135" type="#_x0000_t75" style='width:202.8pt;height:126pt' o:ole="">
<v:imagedata src="./ex5.files/image068.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=270 height=168
src="./ex5.files/image069.gif" v:shapes="_x0000_i1135"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1135"
DrawAspect="Content" ObjectID="_1069593297">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal style='margin-left:21.0pt;text-indent:-21.0pt;mso-list:l1 level1 lfo4;
tab-stops:list 21.0pt'><![if !supportLists]><b><span lang=EN-US>12.<span
style='font:7.0pt "Times New Roman"'> </span></span></b><![endif]><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>若</span><span lang=EN-US>A</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>是</span><sub><span lang=EN-US><!--[if gte vml 1]><v:shape
id="_x0000_i1052" type="#_x0000_t75" style='width:40.8pt;height:16.2pt'>
<v:imagedata src="./ex5.files/image070.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=55 height=22
src="./ex5.files/image071.gif" v:shapes="_x0000_i1052"><![endif]></span></sub><span
lang=EN-US>-</span></b><b><span style='font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>设计的区组矩阵，证明：</span><span
lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal style='margin-left:21.0pt'><b><span lang=EN-US>(a)A</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>的任何一列正好有</span><span lang=EN-US>k</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>个元素；</span><span lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><span style='mso-tab-count:1'> </span>(b)A</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>的任何两列恰好有</span><sub><span lang=EN-US><!--[if gte vml 1]><v:shape
id="_x0000_i1053" type="#_x0000_t75" style='width:10.8pt;height:13.8pt'>
<v:imagedata src="./ex5.files/image072.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=14 height=19
src="./ex5.files/image073.gif" v:shapes="_x0000_i1053"><![endif]></span></sub></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>行有相同的元素。</span><span lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>解：</span></b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>参见书</span><span
lang=EN-US>p254</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>的证明。</span> </p>
<p class=MsoNormal><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
<p class=MsoNormal><b><span lang=EN-US>13</span></b><b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>．已知生成矩阵为</span><span
lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><span style='mso-tab-count:1'> </span><sub><!--[if gte vml 1]><v:shape
id="_x0000_i1054" type="#_x0000_t75" style='width:2in;height:1in'>
<v:imagedata src="./ex5.files/image074.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=192 height=96
src="./ex5.files/image075.gif" v:shapes="_x0000_i1054"><![endif]></sub><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><span style='mso-tab-count:1'> </span></span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>求相应的校验矩阵</span><span lang=EN-US>H.<o:p></o:p></span></b></p>
<p class=MsoNormal><b><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>解：</span></b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>实际上，如果</span><span
lang=EN-US><span style='mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1157" type="#_x0000_t75" style='width:57pt;height:16.8pt' o:ole="">
<v:imagedata src="./ex5.files/image076.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=76 height=23
src="./ex5.files/image077.gif" v:shapes="_x0000_i1157"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1157"
DrawAspect="Content" ObjectID="_1069593298">
</o:OLEObject>
</xml><![endif]--></span><span style='font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，那么</span><span
lang=EN-US><span style='mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1156" type="#_x0000_t75" style='width:64.8pt;height:18pt' o:ole="">
<v:imagedata src="./ex5.files/image078.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=86 height=24
src="./ex5.files/image079.gif" v:shapes="_x0000_i1156"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1156"
DrawAspect="Content" ObjectID="_1069593299">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=MsoNormal><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>所以</span><span lang=EN-US><span
style='mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1165"
type="#_x0000_t75" style='width:142.8pt;height:55.8pt' o:ole="">
<v:imagedata src="./ex5.files/image080.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=190 height=75
src="./ex5.files/image081.gif" v:shapes="_x0000_i1165"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1165"
DrawAspect="Content" ObjectID="_1069593300">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US>14</span></b><b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>．已知校验矩阵</span><span
lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal style='margin-left:21.0pt'><b><sub><span lang=EN-US><!--[if gte vml 1]><v:shape
id="_x0000_i1055" type="#_x0000_t75" style='width:2in;height:55.8pt'>
<v:imagedata src="./ex5.files/image082.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=192 height=74
src="./ex5.files/image083.gif" v:shapes="_x0000_i1055"><![endif]></span></sub><span
lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal style='margin-left:21.0pt'><b><span style='font-family:宋体;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>求相应的生成矩阵。</span><span
lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>解：</span></b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>同上知道：</span></p>
<p class=MsoNormal><span lang=EN-US><span style='mso-text-raise:-33.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1166" type="#_x0000_t75" style='width:142.8pt;height:1in' o:ole="">
<v:imagedata src="./ex5.files/image084.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=190 height=96
src="./ex5.files/image085.gif" v:shapes="_x0000_i1166"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1166"
DrawAspect="Content" ObjectID="_1069593301">
</o:OLEObject>
</xml><![endif]--></span></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US>15</span></b><b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>．已知生成矩阵</span><sub><span
lang=EN-US style='mso-text-raise:-15.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1056"
type="#_x0000_t75" style='width:109.2pt;height:36pt'>
<v:imagedata src="./ex5.files/image086.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=145 height=48
src="./ex5.files/image087.gif" v:shapes="_x0000_i1056"><![endif]></span></sub></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>的码字：</span><span lang=EN-US>00000</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>，</span><span lang=EN-US>01011</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>，</span><span lang=EN-US>11101</span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>，</span><span lang=EN-US>10110<o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><span style='mso-tab-count:1'> </span></span></b><b><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>是分别译出它们的原文。</span><span lang=EN-US><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>解：</span></b><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>先求出它的生成矩阵</span><span
lang=EN-US><span style='mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1179" type="#_x0000_t75" style='width:111pt;height:55.8pt' o:ole="">
<v:imagedata src="./ex5.files/image088.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=148 height=74
src="./ex5.files/image089.gif" v:shapes="_x0000_i1179"><![endif]></span><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1179"
DrawAspect="Content" ObjectID="_1069593302">
</o:OLEObject>
</xml><![endif]--></span><span style='font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，那么可以求出</span><span
lang=EN-US>R</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>的</span> <span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>校验子</span><span
lang=EN-US>S=HR<sup>T</sup></span><span style='font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>：</span></p>
<p class=MsoNormal><span lang=EN-US>00000: S = 0,</span><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>传输正确</span><span
lang=EN-US>,</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>原文是</span><span lang=EN-US>00.</span></p>
<p class=MsoNormal><span lang=EN-US>01011: S = 0,</span><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>传输正确</span><span
lang=EN-US>,</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>原文是</span><span lang=EN-US>01.</span></p>
<p class=MsoNormal><span lang=EN-US>11101: S = 0,</span><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>传输正确</span><span
lang=EN-US>,</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>原文是</span><span lang=EN-US>11.</span></p>
<p class=MsoNormal><span lang=EN-US>10110: S = 0,</span><span style='font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>传输正确</span><span
lang=EN-US>,</span><span style='font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>原文是</span><span lang=EN-US>10.</span></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
<p class=MsoNormal><b><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p>
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