Linear code: Difference between revisions

Revision as of 22:42, 13 May 2005

Revision as of 22:03, 17 June 2005

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:<math>\mathbb{F}^n_2</math>.

Aside: <math>\mathbb{F}^n_2_2 = \{0,1\}</math> is the [[field (mathematics)|field]] of two [[element (mathematics)|element]]s and <math>\mathbb{F}^n_2</math> is the set of all [[n-tuple]]s of length <math>n</math> over <math>\mathbb{F}_2</math>. Occasionally some other [[finite field]] <math>\mathbb{F}_q</math> containing <math>q > 2</math> elements is used, in which case the code is said to be a "''q''-ary" code (rather than a binary code). Special exceptions to the general [[adjective]] "q-ary" are ''binary'' and ''ternary'' codes (corresponding to ''q=2'' and ''q=3'' respectively).

==Properties==