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{{for|players of both rugby codes|List of dual-code rugby internationals}}
== I want to ask you a few very embarrassing thing ==


In [[coding theory]], the '''dual code''' of a [[linear code]]  
'Leave him ...... I'll ask you one, you really want the crooks to justice it?' Li Mei [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペード 財布 通販] asked.<br><br>'Of course ...... I can not wait to kill him, I told him so well, are [http://www.dmwai.com/webalizer/kate-spade-8.html マザーズバッグ ケイトスペード] willing to put heart to him, but he was to tens of thousands of dollars, lie to [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード 人気バッグ] me ...... woo.' Yang Ye grief, all of a sudden wail scrambled.<br><br>Li Mei stroking her shoulders, straight was crying a little lighter, a small channel with her: 'This play with emotion, he should be duly punished, we have found clues ...... Next, I want to ask you a few very embarrassing thing, you are willing to talk to me? very likely through this clue to find him. '<br><br>Yang Ye wiping away tears, looked slightly puzzled Li Mei, [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ アウトレット] also look jing police stationed outside the door for so much as her busy, she felt faint heart touched, wipe tears, calm way forward : 'Sister, I believe you ...... you ask it, to the last, and I have nothing embarrassing.'<br><br>'your trust, there will be [http://www.dmwai.com/webalizer/kate-spade-0.html ハンドバッグ ケイトスペード] a return, I want to ask is that you xing thing .........'
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:<math>C\subset\mathbb{F}_q^n</math>
== For example ==


is the linear code defined by
Like ...... just [http://www.dmwai.com/webalizer/kate-spade-10.html ケイトスペード 財布 セール] like the first hand the kind of bully, one night, stealing more than a [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ 激安] dozen plates and give you a call on the window, to retrieve the license plate is not it, for a hundred dollars and I tell you where to find, than you save more ...... go through a driver for fear of difficulty mentality, a lot of really fighting. [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペードショルダーバッグ新作] Encounter disloyal to you, met disloyal, no amount to fifty, you say give or not to give? Chain fraud, Mozhun victim mentality. Xiaomeng [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード マザーズバッグ] Qi wondering, this case seems more like an upgraded version of Xian Rentiao, and added to the anesthesia robbery, fraud added to the secondary, compared to the old-fashioned hand, [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード クラッチバッグ] more technology, more hidden spacious.<br><br>For example, on one side so hurry, and after careful makeup, but even the victim can not tell the suspect's facial features accurately.<br><br>do not, big bowls dumbfounded at this time, emerged on the computer screen 骆家龙 body as seven or eight women, all of a sudden see this cargo bite the hand index finger, mouth Flows, a pair of gentlemen look.<br><br>'carefully identify what, there are no suspects you've ever seen.' Luo Jialong politely asked.
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:<math>C^\perp = \{x \in \mathbb{F}_q^n \mid \langle x,c\rangle = 0\;\forall c \in C \} </math>
== so I should be directly put ==


where
Surprisingly, riding a broken bike, it was said that he show, but had denied doing so many shows are really not easy, many students long after graduation, back to school looking at [http://www.dmwai.com/webalizer/kate-spade-13.html kate spade ハンドバッグ] old principal remains the same, but also Christine respectful King to call a 'Wang.'<br><br>Yes, he was once a professional criminal investigation traces test instructor, Zhibian two decades, under the [http://www.dmwai.com/webalizer/kate-spade-8.html マザーズバッグ ケイトスペード] command of the police in a lot of celebrities out, such as a detective in the name of Xu Pingqiu, such as [http://www.dmwai.com/webalizer/kate-spade-0.html ケイトスペード中古バッグ] the memory of the heroes Shao [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペードバッグセール] Bing province's mountains, such as are still Council Secretary bits are his students.<br><br>he stood up, [http://www.dmwai.com/webalizer/kate-spade-8.html マザーズバッグ ケイトスペード] accustomed to standing speech, who rarely led shelf, he took the microphone, looked a current student, always unscripted speech, has been talking about his life, and he cleared his throat and said:<br><br>'Students, remember the entrance ceremony, my first words yes, I am your president Wang Lan, congratulations admitted to the police academy.<br><br>Today, I am still president, you will no longer be students, so I should be directly put, Congratulations, graduate. Although many people are under false pretenses, and
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:<math>\langle x, c \rangle = \sum_{i=1}^n x_i c_i </math>
== helpless authentic sentence ==


is a scalar product. In [[linear algebra]] terms, the dual code is the [[Annihilator_(ring_theory)|annihilator]] of ''C'' with respect to the [[bilinear form]] <,>. The [[Dimension_(vector_space)|dimension]] of ''C'' and its dual always add up to the length ''n'':
Not convinced, give Shao Okavango call, but the phone said a few words, dejected expression on his face is very strong, Dong Shaojun know to die, he answered the phone, whispered a few words, and then snapped a press phone jack throw to Wu Guangyu, helpless authentic sentence:<br><br>'slut, you win.'<br><br>'Hey Hey, let's go.' I sin of pride authentic.<br><br>Wu Guangyu slightly reluctantly, and return the car to the fourth prison.<br><br>homework that day, but spared from the afternoon talking about the evening, and then [http://www.dmwai.com/webalizer/kate-spade-8.html kate spade 財布 ゴールド] there took place in the Arabian Nights, and even talk about discipline in the department is also impatient, until late at night a few people left fourth prison, but from the thief mouth where to get more names and nicknames, cattle traders, selling [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード 財布 新作] veterinary drugs, mule animal fur market and the closing of this strange world, in gradually to [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード 人気バッグ] several small police did not know to start his hideous face when they once again set foot [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード マザーズバッグ] on search time, not become strong and courageous, but rather become more hesitant and confused.<br><br>next [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード リボン バッグ] morning, another accident occurred, and a
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:<math>\dim C + \dim C^\perp = n.</math> 
== dumbfounding to cater to the boss ==


A [[generator matrix]] for the dual code is a [[parity-check matrix]] for the original code and vice versa. The dual of the dual code is always the original code.
The. 'Xu Pingqiu laughed.<br><br>more and more outrageous, Shike Zhang simply do not ask, but look Xu Director so got the idea, he was a little laughing, such as a cigarette effort, they appear to pick fights student's car out, is a large body of work Security Section, the two maintained did not move, watching the cars go out very far, just to twist the key Shike Zhang launch, only to be promised at number one pressed, he looked gestured: 'Look, say what was [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペード リボン バッグ] . '<br><br>Hey Hey, gate driving fast in a few bikes out, chasing [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード バッグ 通販] the car in the direction to walk in sin is more than most before picking [http://www.dmwai.com/webalizer/kate-spade-12.html ケイトスペード ハンドバッグ] up the ass of a pull people, a dozen, it looks like not seek trouble-shirts are there will be something else.<br><br>'Let the periphery, holiday tune several of today's field, to see what they were doing. suck, do not look at me, this is for security reasons, in case these Lengxiao Zi did not re-play of light to how to [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード バッグ ショルダー] do things? '<br><br>Xu Pingqiu way forward, pretending to be serious, but the taste is very strong to see a joke, Shike Zhang be silent, dumbfounding to cater to [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード マザーズバッグ] the boss, touched the phone, United
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==Self-dual codes==
== 'little wind ...... Yu Suochang ......' ==
A '''self-dual code''' is one which is its own dual. This implies that ''n'' is even and dim ''C'' = ''n''/2. If a self-dual code is such that each codeword's weight is a multiple of some constant <math>c > 1</math>, then it is of one of the following four types:<ref>{{cite book | last=Conway | first=J.H. | authorlink=John Horton Conway | coauthors=Sloane,N.J.A. | authorlink2=Neil Sloane | title=Sphere packings, lattices and groups | series=Grundlehren der mathematischen Wissenschaften | volume=290 | publisher=[[Springer-Verlag]] | date=1988 | isbn=0-387-96617-X | page=77}}</ref>
*'''Type I''' codes are binary self-dual codes which are not [[doubly even code|doubly even]]. Type I codes are always [[even code|even]] (every codeword has even [[Hamming weight]]).
*'''Type II''' codes are binary self-dual codes which are doubly even.
*'''Type III''' codes are ternary self-dual codes. Every codeword in a Type III code has Hamming weight divisible by 3.
*'''Type IV''' codes are self-dual codes over '''F'''<sub>4</sub>. These are again even.


Codes of types I, II, III, or IV exist only if the length ''n'' is a multiple of 2, 8, 4, or 2 respectively.
Given what misfortune. 'I do not know sin, but he felt this strange change, it seems, and there are some things to check links.<br><br>walked nobody, and when [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード 財布 ゴールド] you look back over [http://www.dmwai.com/webalizer/kate-spade-9.html バッグ ケイトスペード] the crime, Li Yifeng would then look at him, angry over sin understand the moment, smiled, and quickly apologized. Lie Lie Li Yifeng curse up, straight emphasized the:. 'Can not slander me ah, although my father often beat me, but I'm still reluctant to betray him [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード マザーズバッグ] drop'<br><br>'Oh, feeling very concentrated so dense? did not find ah.' I sin road.<br><br>'That, of course, thanks to my father, [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード リボン バッグ] I bear the culprits should not an old guy, what am I going to fight with people.' Li Yifeng [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード 財布 新作] road, I hear the crime is boring to laugh a little while.<br><br>'little wind ...... Yu Suochang ......'<br><br>someone shouted, and put on the car to be more than just crime and Li Yifeng called next, is Yuan captain, he ran out from the office, to the front of the two men, curiously asked: '?'ll go.'<br><br>'ah, to try his luck.' I sin road.<br><br>'right, the afternoon before the opening
 
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==References==
<ul>
{{reflist}}
 
{{refbegin}}
  <li>[http://www.fenchurch.org/priv_cgi-bin/ids/postcomment/commentviewer.cgi http://www.fenchurch.org/priv_cgi-bin/ids/postcomment/commentviewer.cgi]</li>
* {{cite book | last=Hill | first=Raymond | title=A first course in coding theory | publisher=[[Oxford University Press]] | series=Oxford Applied Mathematics and Computing Science Series | date=1986 | isbn=0-19-853803-0 | page=67 }}
 
* {{cite book | last = Pless | first = Vera | authorlink=Vera Pless | title = Introduction to the theory of error-correcting codes | publisher = [[John Wiley & Sons]]|series = Wiley-Interscience Series in Discrete Mathematics | date = 1982| isbn = 0-471-08684-3 | page=8 }}
  <li>[http://www.52813.cc/thread-22063-1-1.html http://www.52813.cc/thread-22063-1-1.html]</li>
* {{cite book | author=J.H. van Lint | title=Introduction to Coding Theory | edition=2nd ed | publisher=Springer-Verlag | series=[[Graduate Texts in Mathematics|GTM]] | volume=86 | date=1992 | isbn=3-540-54894-7 | page=34}}
 
{{refend}}
  <li>[http://www.harariach.com/cgi-bin/hararhistory.cgi http://www.harariach.com/cgi-bin/hararhistory.cgi]</li>
 
 
== External links ==
</ul>
* [http://www.maths.manchester.ac.uk/~pas/code/notes/part9.pdf MATH32031: Coding Theory - Dual Code] - pdf with some examples and explanations
 
[[Category:Coding theory]]

Revision as of 01:19, 4 March 2014

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someone shouted, and put on the car to be more than just crime and Li Yifeng called next, is Yuan captain, he ran out from the office, to the front of the two men, curiously asked: '?'ll go.'

'ah, to try his luck.' I sin road.

'right, the afternoon before the opening 相关的主题文章: