Tricolore 3-designs in Type III codes

@article{Bonnecaze2001Tricolore3I,
  title={Tricolore 3-designs in Type III codes},
  author={Alexis Bonnecaze and Patrick Sol{\'e} and Parampalli Udaya},
  journal={Discrete Mathematics},
  year={2001},
  volume={241},
  pages={129-138}
}
A split complete weight enumerator in six variables is used to study the 3-colored designs held by codewords of xed composition in Type III codes containing the all-one codeword. In particular the ternary Golay code contains 3-colored 3-designs. We conjecture that every weight class in a Type III code with the all-one codeword holds 3-colored 3-designs.