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2013-02-27T08:02:07Z

Bot: Migrating 6 interwiki links, now provided by Wikidata on d:q650001 (Report Errors)

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	~~The author~~ is ~~known by~~ the ~~title~~ of ~~Numbers Lint~~. ~~Hiring~~ is ~~her day occupation now but she~~'~~s usually needed her own company~~. ~~What I adore doing~~ is ~~doing ceramics but I haven~~'~~t produced~~ a ~~dime with it~~. ~~For~~ a ~~while she's been in South Dakota~~.<br><br>~~Also visit my site~~: ~~at home std testing;~~ [http://~~Www~~.~~Hotporn123~~.com/~~blog/150819 simply click the up coming internet site~~],		{{For\|generator matrices in probability theory\|transition rate matrix}}
			In [[coding theory]], a '''generator matrix''' is a [[Basis (linear algebra)\|basis]] for a [[linear code]], generating all its possible codewords.
			If the matrix is ''G'' and the linear code is ''C'',
			:''w'' = '''c'''G
			where ''w'' is a [[codeword]] of the linear code ''C'', '''c''' is a row vector, and a [[bijection]] exists between ''w'' and '''c'''. A generator matrix for an (<math>n</math>, <math>M = q^k</math>, <math>d</math>)<sub><math>q</math></sub>-code has dimensions ''k''×''n''. Here ''n'' is the length of a codeword, ''k'' is the number of information bits, ''d'' is the minimum distance of the code, and ''q'' is the number of symbols in the alphabet (thus, ''q'' = 2 indicates a [[binary code]], etc.). The number of [[Redundancy (information theory)\|redundant bits]] is denoted by ''r = n - k''.

			The [[Systematic code\|systematic]] form for a generator matrix is
			: <math>G = \begin{bmatrix} I_k \| P \end{bmatrix}</math>
			where <math>I_k</math> is a ''k''×''k'' [[identity matrix]] and P is of dimension ''k''×''r''.

			A generator matrix can be used to construct the [[parity check matrix]] for a code (and vice-versa).

			==Equivalent Codes==
			Codes C<sub>1</sub> and C<sub>2</sub> are equivalent (denoted C<sub>1</sub> ~ C<sub>2</sub>) if one code can be created from the other via the following two transformations:

			# permute components, and
			# scale components.

			Equivalent codes have the same distance.

			The generator matrices of equivalent codes can be obtained from one another via the following transformations:

			# permute rows
			# scale rows
			# add rows
			# permute columns, and
			# scale columns.

			==See also==
			* [[Hamming code (7,4)]]

			==External links==
			* [http://mathworld.wolfram.com/GeneratorMatrix.html MathWorld entry]

			{{DEFAULTSORT:Generator Matrix}}
			[[Category:Coding theory]]

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2012-06-19T14:22:02Z

Robot: Adding tr:Süper yıldız kümesi

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The author is known by the title of Numbers Lint. Hiring is her day occupation now but she's usually needed her own company. What I adore doing is doing ceramics but I haven't produced a dime with it. For a while she's been in South Dakota.<br><br>Also visit my site: at home std testing; [http://Www.Hotporn123.com/blog/150819 simply click the up coming internet site],

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