en>Mebden: /* Dominated strategies */

2014-08-19T06:20:57Z

Dominated strategies

en>Toni 001: changed link from "Nash equilibria" to "Nash equilibrium"

2013-12-12T21:01:21Z

changed link from "Nash equilibria" to "Nash equilibrium"

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	~~I woke up yesterday and~~ [~~https://Www.google.com/search?hl=en&gl=us&tbm=nws&q=realised+-&btnI=lucky realised -~~] ~~I've been solitary for a little while now and after much bullying from friends I today find myself [http://lukebryantickets.asiapak.net Luke Bryan Save The Date~~] ~~opted for internet dating. They assured me that there are plenty of pleasant~~, ~~normal and interesting folks to fulfill, so here goes~~ the pitch!<br>I attempt to keep as physically healthy as possible staying at the fitness center several-times per week. I love my sports and try to perform or view since many a possible. I am going to frequently at Hawthorn matches being wintertime. Notice: I'~~ve seen the carnage~~ of ~~fumbling matches at stocktake sales, Supposing that you really contemplated shopping~~ a ~~hobby I really don't brain.<br>My buddies and family are magnificent and hanging out with them at pub gigabytes or dinners is obviously vital. I have never 2014 luke Bryan tour (~~[~~http://www.ladyhawkshockey.org www.ladyhawkshockey.org~~]~~) been in to nightclubs as I locate you could do not get a significant conversation together with~~ the ~~noise. I also got two definitely cheeky and very~~ [~~http://Www.Cunningpuppies.com/ cunning puppies~~] ~~who are invariably ready to meet up fresh individuals~~.~~<br><br>~~		In [[coding theory]], the '''weight enumerator polynomial''' of a binary [[linear code]] specifies the number of words of each possible [[Hamming weight]].

	~~my web blog~~ :: [~~http~~://~~okkyunglee~~.~~com vip tickets~~ to ~~luke bryan~~]		Let <math>C \subset \mathbb{F}_2^n</math> be a binary linear code length <math>n</math>. The '''weight distribution''' is the sequence of numbers

			:<math> A_t = \#\{c \in C \mid w(c) = t \} </math>

			giving the number of [[codeword]]s ''c'' in ''C'' having weight ''t'' as ''t'' ranges from 0 to ''n''. The '''weight enumerator''' is the bivariate [[polynomial]]

			:<math> W(C;x,y) = \sum_{w=0}^n A_w x^w y^{n-w}.</math>

			==Basic properties==
			#<math> W(C;0,1) = A_{0}=1 </math>
			#<math> W(C;1,1) = \sum_{w=0}^{n}A_{w}=\|C\| </math>
			#<math> W(C;1,0) = A_{n}= 1 \mbox{ iff } (1,\ldots,1)\in C\ \mbox{ and } 0 \mbox{ otherwise.} </math>
			#<math> W(C;1,-1) = \sum_{w=0}^{n}A_{w}(-1)^{n-w} = A_{n}+(-1)^{1}A_{n-1}+\ldots+(-1)^{n-1}A_{1}+(-1)^{n}A_{0} </math>

			==MacWilliams identity==
			Denote the [[dual code]] of <math>C \subset \mathbb{F}_2^n</math> by

			:<math>C^\perp = \{x \in \mathbb{F}_2^n \,\mid\, \langle x,c\rangle = 0 \mbox{ }\forall c \in C \} </math>

			(where <math><,></math> denotes the vector [[dot product]] and which is taken over <math>\mathbb{F}_2</math>).

			The '''MacWilliams identity''' states that

			:<math>W(C^\perp;x,y) = \frac{1}{\mid C \mid} W(C;y-x,y+x). </math>

			The identity is named after [[Jessie MacWilliams]].

			==Distance enumerator==
			The '''distance distribution''' or '''inner distribution''' of a code ''C'' of size ''M'' and length ''n'' is the sequence of numbers

			:<math> A_i = \frac{1}{M} \# \left\lbrace (c_1,c_2) \in C \times C \mid d(c_1,c_2) = i \right\rbrace </math>

			where ''i'' ranges from 0 to ''n''. The '''distance enumerator polynomial''' is

			:<math> A(C;x,y) = \sum_{i=0}^n A_i x^i y^{n-i} </math>

			and when ''C'' is linear this is equal to the weight enumerator.

			The '''outer distribution''' of ''C'' is the 2<sup>''n''</sup>-by-''n''+1 matrix ''B'' with rows indexed by elements of GF(2)<sup>''n''</sup> and columns indexed by integers 0...''n'', and entries

			:<math> B_{x,i} = \# \left\lbrace c \in C \mid d(c,x) = i \right\rbrace . </math>

			The sum of the rows of ''B'' is ''M'' times the inner distribution vector (''A''<sub>0</sub>,...,''A''<sub>''n''</sub>).

			A code ''C'' is '''regular''' if the rows of ''B'' corresponding to the codewords of ''C'' are all equal.

			==References==
			* {{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 \| pages=165–173 }}
			* {{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 \| pages=103–119 }}
			* {{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 }} Chapters 3.5 and 4.3.

			[[Category:Coding theory]]
			[[Category:Error detection and correction]]
			[[Category:Mathematical identities]]

en>SchreiberBike: Repairing links to disambiguation pages - You can help! - Graph

2012-08-08T15:33:15Z

Repairing links to disambiguation pages - You can help! - Graph

New page

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en>Mebden: /* Dominated strategies */

en>Toni 001: changed link from "Nash equilibria" to "Nash equilibrium"

en>SchreiberBike: Repairing links to disambiguation pages - You can help! - Graph