Tricolore 3-designs in Type III codes Original Research Article

A split complete weight enumerator in six variables is used to study the 3-colored designs held by codewords of fixed 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.