EXTREMAL BINARY SELF-DUAL CODES OF LENGTHS 42 AND 44 WITH NEW WEIGHT ENUMERATORS

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 $ mathbf{36} $ (1990), 1319-1333) gives the putative weight enumerators of extremal self-dual binary codes for lengths $ n leqq 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