A lexicode of minimum distancelength ''dn'' and lengthminimum distance ''nd'' 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"
Line 774:
|}
All odd d-bit distancelexicode lexicodesdistances are exact copies of the even d+1 bit distancedistances minus the last dimension, so
an odd-dimensional space can never create something new or more interesting than the d+1 even-dimensional space above.
