Greedy Codes

Given an ordered basis of F/sup n//sub 2/ and an integer d, we define a greedy algorithm for constructing a code of minimum distance at least d. We show that these greedy codes are linear and construct a parity check matrix for them. A special case of this algorithm gives the lexicodes, thereby providing a proof of their linearity which is independent of game theory. For ordered bases which have a triangular form we are able to give a lower bound on the dimension of greedy codes. Some greedy codes are better than lexicodes.