Shriek map - Revision history

en>AnomieBOT: Dating maintenance tags: {{Mergeto}}

2014-12-27T06:08:40Z

Dating maintenance tags: {{Mergeto}}

← Older revision		Revision as of 08:08, 27 December 2014
Line 1:		Line 1:
	~~The '''Hamming scheme''', named after [[Richard Hamming]], is also known as~~ the ~~'''hyper-cubic association scheme''', and it is~~ the ~~most important example for [[coding theory]]~~.~~<ref>P. Delsarte and V~~. I. Levenshtein, “Association schemes and coding theory,“ ''IEEE Trans. Inform. Theory'', vol. 44, no. 6, pp. 2477–2504, 1998.</ref><ref>P. Camion, "Codes and Association Schemes: Basic Properties of Association Schemes Relevant to Coding," in ~~''Handbook of Coding Theory''~~, ~~V. S. Pless~~ and W. ~~C. Huffman~~, ~~Eds~~.~~, Elsevier, The Netherlands, 1998.</ref><ref>F. J. MacWilliams~~ and ~~N. J. A. Sloane, ''The Theory of Error~~-~~Correcting Codes'', Elsevier, New York, 1978.</ref> In this scheme <math>X=\mathcal{F}^n</math>, the set~~ of ~~binary vectors of length <math>n</math>,~~ and ~~two vectors <math>x</math>, <math>y\in \mathcal{F}^n</math> are <math>i</math>-th associates if they~~ have ~~[[Hamming distance]]~~ <~~math~~>i<~~/math~~> ~~apart.~~		CMS provides the best platform to create websites that fulfill all the specifications of SEO. Medical word press themes give you the latest medical designs. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. Word - Press also provides protection against spamming, as security is a measure issue. Also our developers are well convergent with the latest technologies and bitty-gritty of wordpress website design and promises to deliver you the best solution that you can ever have. <br><br>

	~~Recall~~ that ~~an [[association scheme]] is visualized as~~ a ~~[[complete graph]] with labeled edges~~. ~~The graph has <math>v</math> vertices, one for each point~~ of ~~<math>X</math>~~, ~~and the edge joining vertices~~ <~~math~~>x<~~/math~~> and ~~<math>y<~~/~~math> is labeled <math>i<~~/~~math> if <math>x<~~/~~math> and <math>y</math> are <math>i</math>-th associates~~. ~~Each edge has a unique label~~, and the ~~number~~ of ~~triangles with a fixed base labeled <math>k</math> having~~ the ~~other edges labeled <math>i</math> and <math>j</math> is a constant <math>c_{ijk}</math>, depending on <math>i,j,k</math> but not on~~ the ~~choice~~ of the ~~base~~. ~~In particular~~, each ~~vertex is incident with exactly <math>c_{ii0}=v_{i}~~<~~/math~~> ~~edges labeled~~ <~~math>i</math>; <math>v_{i}</math~~> is ~~the [[Adjacency relation\|valency]]~~ of ~~the [[Relation (mathematics)\|relation]] <math>R_{i}</math>~~.		purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. This plugin allows a blogger get more Facebook fans on the related fan page. By purchasing Word - Press weblogs you can acquire your very own domain title and have total command of your web site. But in case you want some theme or plugin in sync with your business needs, it is advisable that you must seek some professional help. <br><br>If you loved this information and you wish to receive much more information about [http://snipitfor.me/backup_plugin_4444782 backup plugin] please visit our own site. Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. You or your web designer can customize it as per your specific needs. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. Quttera - Quttera describes itself as a 'Saa - S [Software as a Service] web-malware monitoring and alerting solution for websites of any size and complexity. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. Look for experience: When you are searching for a Word - Press developer you should always look at their experience level. <br><br>Instead, you can easily just include it with our bodies integration field in e - Panel. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. Word - Press is an open source content management system which is easy to use and offers many user friendly features. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins.
	~~The <math>c_{ijk}</math> in~~ a '~~''Hamming scheme''' are given by~~

	~~: <math>c_{ijk} = \begin{cases}~~
	~~\dbinom{k}{\frac{i~~-~~j+k}{2}}\dbinom{n~~-~~k}{\frac{i+j~~-~~k}{2}}~~, ~~& \text{if } i+j~~-~~k \text{ is even~~,~~} \\~~
	~~\;\;\;\;\;\;\;\;\;\;0\;\;\;\;\;\;\;\;\;\;\;~~,~~\;\; & \text{if } i+j~~-~~k \text{ is odd~~.~~} \end{cases}~~ <~~/math~~>

	~~Here,~~ <~~math~~>~~v=\left\|X\right\|=2^{n}</math> and <math>v_{i}=\binom{n}{i}</math>. The [[Matrix (mathematics)\|matrices]]~~ in ~~the [[Bose–Mesner algebra\|Bose~~-~~Mesner algebra]] are <math>2^{n}\times 2^{n}</math> [[Matrix (mathematics)\|matrices]]~~, ~~with rows~~ and ~~columns labeled by vectors <math>x\~~in ~~\mathcal{F}^{n}</math>~~. ~~In particular the <math>\left(x~~,~~y\right)</math>~~-~~th entry of <math>D_{k}</math>~~ is ~~<math>1</math> if~~ and only if
	~~<math>d_{H}(x~~,~~y)=k</math>~~.

	~~==References==~~
	~~{{reflist}}~~

	~~{{DEFAULTSORT:Hamming Scheme}}~~
	~~[[Category:Coding theory]]~~

en>BattyBot: changed {{Unreferenced}} to {{Refimprove}} & general fixes using AWB

2013-11-11T03:37:36Z

changed {{Unreferenced}} to {{Refimprove}} & general fixes using AWB

← Older revision		Revision as of 05:37, 11 November 2013
Line 1:		Line 1:
	~~Im addicted to my hobby Travel~~. ~~Appears boring? Not!~~<br>I ~~also~~ to ~~learn Turkish~~ in ~~my spare time~~.<br><br>~~My page~~; [~~http~~://~~tinyurl~~.~~com~~/~~pch83be cheap ugg boots~~]		The '''Hamming scheme''', named after [[Richard Hamming]], is also known as the '''hyper-cubic association scheme''', and it is the most important example for [[coding theory]].<ref>P. Delsarte and V. I. Levenshtein, “Association schemes and coding theory,“ ''IEEE Trans. Inform. Theory'', vol. 44, no. 6, pp. 2477–2504, 1998.</ref><ref>P. Camion, "Codes and Association Schemes: Basic Properties of Association Schemes Relevant to Coding," in ''Handbook of Coding Theory'', V. S. Pless and W. C. Huffman, Eds., Elsevier, The Netherlands, 1998.</ref><ref>F. J. MacWilliams and N. J. A. Sloane, ''The Theory of Error-Correcting Codes'', Elsevier, New York, 1978.</ref> In this scheme <math>X=\mathcal{F}^n</math>, the set of binary vectors of length <math>n</math>, and two vectors <math>x</math>, <math>y\in \mathcal{F}^n</math> are <math>i</math>-th associates if they have [[Hamming distance]] <math>i</math> apart.

			Recall that an [[association scheme]] is visualized as a [[complete graph]] with labeled edges. The graph has <math>v</math> vertices, one for each point of <math>X</math>, and the edge joining vertices <math>x</math> and <math>y</math> is labeled <math>i</math> if <math>x</math> and <math>y</math> are <math>i</math>-th associates. Each edge has a unique label, and the number of triangles with a fixed base labeled <math>k</math> having the other edges labeled <math>i</math> and <math>j</math> is a constant <math>c_{ijk}</math>, depending on <math>i,j,k</math> but not on the choice of the base. In particular, each vertex is incident with exactly <math>c_{ii0}=v_{i}</math> edges labeled <math>i</math>; <math>v_{i}</math> is the [[Adjacency relation\|valency]] of the [[Relation (mathematics)\|relation]] <math>R_{i}</math>.
			The <math>c_{ijk}</math> in a '''Hamming scheme''' are given by

			: <math>c_{ijk} = \begin{cases}
			\dbinom{k}{\frac{i-j+k}{2}}\dbinom{n-k}{\frac{i+j-k}{2}}, & \text{if } i+j-k \text{ is even,} \\
			\;\;\;\;\;\;\;\;\;\;0\;\;\;\;\;\;\;\;\;\;\;,\;\; & \text{if } i+j-k \text{ is odd.} \end{cases} </math>

			Here, <math>v=\left\|X\right\|=2^{n}</math> and <math>v_{i}=\binom{n}{i}</math>. The [[Matrix (mathematics)\|matrices]] in the [[Bose–Mesner algebra\|Bose-Mesner algebra]] are <math>2^{n}\times 2^{n}</math> [[Matrix (mathematics)\|matrices]], with rows and columns labeled by vectors <math>x\in \mathcal{F}^{n}</math>. In particular the <math>\left(x,y\right)</math>-th entry of <math>D_{k}</math> is <math>1</math> if and only if
			<math>d_{H}(x,y)=k</math>.

			==References==
			{{reflist}}

			{{DEFAULTSORT:Hamming Scheme}}
			[[Category:Coding theory]]

en>Citation bot 1: Citations: [Pu177]Tweaked: issue. You can use this bot yourself! Report bugs here.

2010-07-23T15:24:39Z

Citations: [Pu177]Tweaked: issue. You can use this bot yourself! Report bugs here.

New page

Im addicted to my hobby Travel. Appears boring? Not!<br>I also to learn Turkish in my spare time.<br><br>My page; [http://tinyurl.com/pch83be cheap ugg boots]