On some families of binary codes

We give further results on the weight distributions of the two families of binary codes recently constructed by simplicial complexes by (Wu, Lee, 2020), and show that the converse of the above results is also correct, that is, the binary codes with such weight distributions properties must be these two families of codes. Based on the above results, we also construct another family of binary self-orthogonal codes and present their separating properties and applications to the secret sharing scheme, cryptography and other aspects of information security.