Binary optimal linear rate 1/2 codes

In this paper, we complete the classification of binary 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 12 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.