Comparison study of two constructions on linear codes over 𝔽2 using simplicial complexes

The construction of linear codes using simplicial complexes has been a major development for obtaining minimal and optimal linear codes. The advantage of simplicial complexes in the inclusion-exclusion principle has influenced the efficiency of Hamming weight distribution computation. There are two types of linear code constructions that use simplicial complexes over [Formula: see text]. The first is the construction by Chang and Hyun, which is associated with Boolean functions to determine the basis. The second is the construction by Wu and Lee, which employs simplicial complexes as defining sets that act as the basis. The method used by Wu and Lee led to further research in this area. We studied the relationship between the two linear codes over [Formula: see text] in the two constructions using the same simplicial complex. Moreover, we obtain self-orthogonal codes and the generalized Hamming weights formula using the construction with Boolean functions arising from simplicial complexes.