Greedy generation of non-binary codes

We get a B-ordering of all binary n-tuples V/sub n/ by choosing an ordered basis (y/sub 1/, ..., y/sub n/) of V/sub n/ and ordering the n-tuples as follows: 0, y/sub 1/, y/sub 2/, y/sub 2/+y/sub 1/, y/sub 3/, y/sub 3/+y/sub 1/, y/sub 3/+y/sub 2/, y/sub 3/+y/sub 2/+y/sub 1/, y/sub 4/, ... . Given a minimum distance d, choose a set of vectors S with the zero vector first, then go through the vectors in their B-ordering and choose the next vector which has distance d or more from all vectors already chosen. The surprising result that S is linear has been shown in several different ways. Linear codes found in this fashion are called greedy codes. We also look at the non-binary case. One can generalize the concept of B-ordering to the case of an arbitrary base field. We also look at the parity check matrix.