Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2821 2023 2023 Online Islamic University, Department Of Science and Information Technology, Doha, Qatar admin admin In this paper we prove that for any ordered basis  of a vector space there is a basis  for which the greedy code generated using the B-ordering is linear with respect to , where B2 is derived from  by a lower triangular matrix P; . In Addition we prove a similar result for self-orthogonal greedy codes. 2023 2023 25 39 10.54216/PMTCS.030202 https://www.americaspg.com/articleinfo/40/show/2821