Linear code: Difference between revisions

Revision as of 22:33, 12 May 2005

Revision as of 17:33, 13 May 2005

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==Properties==

By virtue of the fact that the code is a [[subspace]] of ''F''^''n'', the sum ''c₁ + c₂'' of two codewords in ''C'' is also a codeword (ie an [[element (mathematics)|element]] of the subspace ''C''). This definition also allows the entire code (which may be very large) to be represented as the [[span (linear algegra)|span]] of a minimialminimal set of codewords (known as a [[basis (linear algebra)|basis]] in [[linear algebra]] terms). These basis codewords are often collated in the rows of a matrix known as a ''generating matrix'' for the code ''C''.

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'''Nota BeneRemark.''': this is not to be confused with the notation [''n'',''r'',''d''] to denote a non-linear code of length ''n'', size ''r'' (ie having ''r'' codewords) and minimum Hamming distance ''d''.