Rectified 5-cell - Revision history

en>Tomruen: /* Alternate names */

2015-01-12T21:03:05Z

Alternate names

← Older revision		Revision as of 23:03, 12 January 2015
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	~~Alyson is what my spouse loves~~ to ~~call me but~~ I ~~don~~'t like ~~when people use my full name~~. To ~~climb~~ is ~~some~~ thing I ~~really appreciate doing~~. I've ~~always loved living~~ in ~~Alaska. He functions as a bookkeeper~~.<br><br>~~Here is~~ my page ~~online~~ psychic ([http://~~www~~.~~seekavideo~~.~~com/playlist/2199/video~~/ http://~~www~~.~~seekavideo~~.~~com~~])		I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. To perform lacross is the thing I love most of all. Since he was 18 he's been operating as an info officer but he plans on changing it. I've usually cherished residing in Kentucky but now I'm contemplating other options.<br><br>Feel free to surf to my page: best psychic readings; [http://isaworld.pe.kr/?document_srl=392088 http://isaworld.pe.kr],

en>Wavelength: inserting 1 hyphen: —> "four-dimensional"—wikt:four-dimensional

2014-03-03T19:56:49Z

inserting 1 hyphen: —> "four-dimensional"—wikt:four-dimensional

← Older revision		Revision as of 21:56, 3 March 2014
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	~~In [[computer science]],~~ ''~~'group codes''' are a type of [[coding theory\|code]]~~. ~~Group codes consist of~~		Alyson is what my spouse loves to call me but I don't like when people use my full name. To climb is some thing I really appreciate doing. I've always loved living in Alaska. He functions as a bookkeeper.<br><br>Here is my page online psychic ([http://www.seekavideo.com/playlist/2199/video/ http://www.seekavideo.com])
	~~<math>n</math> [[linear block codes]] which are subgroups of <math>G^n</math>, where <math>G</math> is~~ a ~~finite [[Abelian group]]~~.

	~~A systematic group code~~ <~~math~~>C<~~/math~~> is a code over <math>G^n</math> of order <math>\left\| G \right\|^k</math> defined by <math>n-k</math> homomorphisms which determine the parity check bits. The remaining <math>k</math> bits are the information bits themselves.

	~~== Construction ==~~
	~~Group codes can be constructed by special~~ [[generator matrix\|generator matrices]] which resemble generator matrices of linear block codes except that the elements of those matrices are [[endomorphism]]s of the group instead of symbols from the code's alphabet. For example, consider the generator matrix

	:~~<math>~~
	~~G = \begin{pmatrix} \begin{pmatrix} 0 0 \\ 1 1 \end{pmatrix} \begin{pmatrix} 0 1 \\ 0 1 \end{pmatrix} \begin{pmatrix} 1 1 \\ 0 1 \end{pmatrix} \\~~
	~~\begin{pmatrix} 0 0 \\ 1 1 \end{pmatrix} \begin{pmatrix} 11 \\ 1 1 \end{pmatrix} \begin{pmatrix} 0 0 \\ 0 0 \end{pmatrix}~~
	~~\end{pmatrix}~~
	</~~math>~~

	~~The elements of this matrix are <math>2\times 2<~~/~~math> matrices which are endomorphisms~~. ~~In this scenario, each codeword can be represented as~~
	~~<math>g_1^{m_1} g_2^{m_2}~~ .~~.. g_r^{m_r}<~~/~~math>~~
	~~where <math>g_1,... g_r<~~/~~math> are the [[Generating set of a group\|generator]]s of <math>G<~~/~~math>.~~

	~~== References ==~~
	* {{cite doi\|10.1109/~~ISIT.1993.748676}}~~
	* G. D. Forney, M. Trott, {{doi-inline\|10.1109/~~18.259635\|The dynamics of group codes : State spaces, trellis diagrams and canonical encoders}}, ''IEEE Trans. Inform. theory'', Vol '''39''' (1993), pages 1491-1593.~~
	* V. V. Vazirani, Huzur Saran and B. S. Rajan, {{doi-inline\|10.1109/~~18.556679\|An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups}}, ''IEEE Trans~~. ~~Inform~~. ~~Theory'' '''42''', No.6, (1996~~)~~, 1839-1854.~~
	* A. A. Zain, B. Sundar Rajan, "Dual codes of Systematic Group Codes over Abelian Groups", ''Appl. Algebra Eng. Commun. Comput.'' '''8'''(1): 71-83 (1996).

	~~[[Category:Coding theory]]~~

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q7303156

2013-03-23T12:38:52Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q7303156

← Older revision		Revision as of 14:38, 23 March 2013
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	~~Hi there~~. ~~My title~~ is ~~Sophia Meagher even though it~~ is ~~not~~ the ~~name on my beginning certificate~~. ~~North Carolina is exactly where we~~'~~ve been residing for years and will never transfer~~. ~~I am really fond~~ of ~~to go to karaoke but I've been using on new issues recently~~. ~~Office supervising is where her primary earnings arrives from~~.<br><br>~~Feel free to surf to my site~~ ... [~~https:~~//~~www~~-~~Ocl~~.~~gist~~.ac.kr/~~work/xe/?document_srl=605236 psychic readers~~]		In [[computer science]], '''group codes''' are a type of [[coding theory\|code]]. Group codes consist of
			<math>n</math> [[linear block codes]] which are subgroups of <math>G^n</math>, where <math>G</math> is a finite [[Abelian group]].

			A systematic group code <math>C</math> is a code over <math>G^n</math> of order <math>\left\| G \right\|^k</math> defined by <math>n-k</math> homomorphisms which determine the parity check bits. The remaining <math>k</math> bits are the information bits themselves.

			== Construction ==
			Group codes can be constructed by special [[generator matrix\|generator matrices]] which resemble generator matrices of linear block codes except that the elements of those matrices are [[endomorphism]]s of the group instead of symbols from the code's alphabet. For example, consider the generator matrix

			:<math>
			G = \begin{pmatrix} \begin{pmatrix} 0 0 \\ 1 1 \end{pmatrix} \begin{pmatrix} 0 1 \\ 0 1 \end{pmatrix} \begin{pmatrix} 1 1 \\ 0 1 \end{pmatrix} \\
			\begin{pmatrix} 0 0 \\ 1 1 \end{pmatrix} \begin{pmatrix} 11 \\ 1 1 \end{pmatrix} \begin{pmatrix} 0 0 \\ 0 0 \end{pmatrix}
			\end{pmatrix}
			</math>

			The elements of this matrix are <math>2\times 2</math> matrices which are endomorphisms. In this scenario, each codeword can be represented as
			<math>g_1^{m_1} g_2^{m_2} ... g_r^{m_r}</math>
			where <math>g_1,... g_r</math> are the [[Generating set of a group\|generator]]s of <math>G</math>.

			== References ==
			* {{cite doi\|10.1109/ISIT.1993.748676}}
			* G. D. Forney, M. Trott, {{doi-inline\|10.1109/18.259635\|The dynamics of group codes : State spaces, trellis diagrams and canonical encoders}}, ''IEEE Trans. Inform. theory'', Vol '''39''' (1993), pages 1491-1593.
			* V. V. Vazirani, Huzur Saran and B. S. Rajan, {{doi-inline\|10.1109/18.556679\|An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups}}, ''IEEE Trans. Inform. Theory'' '''42''', No.6, (1996), 1839-1854.
			* A. A. Zain, B. Sundar Rajan, "Dual codes of Systematic Group Codes over Abelian Groups", ''Appl. Algebra Eng. Commun. Comput.'' '''8'''(1): 71-83 (1996).

			[[Category:Coding theory]]

en>Tomruen: /* Related polytopes */

2012-07-12T03:11:40Z

Related polytopes

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Hi there. My title is Sophia Meagher even though it is not the name on my beginning certificate. North Carolina is exactly where we've been residing for years and will never transfer. I am really fond of to go to karaoke but I've been using on new issues recently. Office supervising is where her primary earnings arrives from.<br><br>Feel free to surf to my site ... [https://www-Ocl.gist.ac.kr/work/xe/?document_srl=605236 psychic readers]