Binary Optimal Linear Rate 1/2 Codes

In this paper, we complete the classi cation of optimal linear [n; n/2] codes up to length 28. We have determined that there are 1535 inequivalent [14,7,4] codes, 1682 inequivalent [20,10,6] codes, and 3 inequivalent [26,13,7] codes. In addition, we show that the smallest length for which an optimal rate 1/2 code has a trivial automorphism group is 14. Double circulant codes which attain the highest known minimum distance are given for lengths up to 64