Lexicographic code: Difference between revisions

Revision as of 18:05, 30 May 2009

Revision as of 18:06, 30 May 2009

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== Construction ==

A lexicode of minimum distance ''d'' and length <math>''n</math>'' over a [[finite field]] <math>\mathbb{F}</math> is generated by starting with the all -zero vector and iteratively adding the next vector (in [[lexicographic order]]) of minimum Hamming distance <math>''d</math>'' from the vectors added so far. As an example, the length <math>-3</math> lexicode of minimum distance <math>2</math> would consist of the vectors marked by an "X" in the following example:

would consist of the vectors marked by an "X" in the following example:

:{| class="wikitable"