2003 Volume 57 Issue 2 Pages 333-345
A paper of Conway and Sloane (J. H. Conway and N. J. A. Sloane. A new upper bound on the minimal distance of self-dual codes. IEEE Trans. Inform. Theory 36 (1990), 1319-1333) gives the putative weight enumerators of extremal self-dual binary codes for lengths n ≤ 64 and n = 72. The construction of such codes with putative weight enumerators has been one of the fundamental problems in coding theory. In this paper, we construct extremal self-dual binary [42, 21, 8] and extremal self-dual binary [44, 22, 8] codes whose weight enumerators are not yet known to exist.