Binary Optimal Linear Rate 1/2 Codes

In this paper, we classify the optimal linear [n, n/2] codes of length upto 12. We show that there is a unique optimal odd formally self-dual [20, 10, 6] code upto equivalence. We also show that at least one optimal linear [n, n/2] code is self-dual or formally self-dual for lengths upto 48 (except 38 and 40).