New binary self-dual codes via a variation of the four-circulant construction

Abstract

In this work, we generalize the four circulant construction for self-dual
codes. By applying the constructions over the alphabets F_2, F_2+uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68.
More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.