Linear code: Difference between revisions

Revision as of 01:39, 24 October 2023

Revision as of 00:20, 15 January 2024

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==Popular notation==

{{main|Block code#Popular notation}}

[[Code]]s in general are often denoted by the letter ''C'', and a code of length ''n'' and of [[dimension (linear algebra)|rank]] ''k'' (i.e., having ''kn'' code words in its basis and ''k'' rows in its ''generating matrix'') is generally referred to as an (''n'', ''k'') code. Linear block codes are frequently denoted as [''n'', ''k'', ''d''] codes, where ''d'' refers to the code's minimum Hamming distance between any two code words.

(The [''n'', ''k'', ''d''] notation should not be confused with the (''n'', ''M'', ''d'') notation used to denote a ''non-linear'' code of length ''n'', size ''M'' (i.e., having ''M'' code words), and minimum Hamming distance ''d''.)