Higher Weights and Binary Self-Dual Codes

The theory of higher weights is applied to binary self-dual codes. Bounds are given for the second minimum higher weight and a Gleason type theorem is derived for the second higher weight enumerator. The second weight enumerator is shown to be unique for the putative [72, 36, 16] Type II code and the first three minimum weights are computed for optimal codes of length less than 28.