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