Linear code: Difference between revisions

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Properties: Regularized in-line expressions. Edited for style.
Popular notation: Regularized in-line expressions and clarified the prose. Long parentheticals interfere with ellipsis, imo.
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==Popular notation==
 
[[Code]]s in general are often denoted by the letter <math>''C</math>''. A linear code of length <math>''n</math>'', of [[dimension (linear algebra)|rank]] <math>''k</math>'' (iei.e., having <math>''k</math>'' code codewordswords in its basis and <math>''k</math>'' rows in its ''generating matrix''), and of minimum Hamming weight <math>''d</math>'' is referred to as an <math>(''n'',&nbsp;''k'',&nbsp;''d'')</math> code.
 
'''Remark.''' This is(''n'',&nbsp;''k'',&nbsp;''d'') notnotation toshould not be confused with the notation <math>[''n'',&nbsp;''r'',&nbsp;''d'']</math> notation used to denote a ''non-linear'' code of length <math>''n</math>'', size <math>''r</math>'' (iei.e., having <math>''r</math>'' codewordscode words), and minimum Hamming distance <math>''d</math>''.
 
==Examples==