We present a construction method for Ramanujan graphs from simplicial complexes with one or two blockers, using the corresponding multivariable functions, where blockers mean minimal elements of the complement of a simplicial complex. First, we completely find all the binary linear codes obtained from simplicial complexes with one or two blockers, producing exactly 23 families of few-weight binary linear codes and 4 families of self-orthogonal codes. Furthermore, their weight distributions are explicitly computed by using the corresponding multivariable functions. Then we construct 14 families of nonbipartite Ramanujan graphs from the few-weight binary linear codes found; their eigenvalues are computed by using the weight distributions of the corresponding codes. We emphasize that it is the first time that the simplicial complexes with a few blockers are used for construction of few-weight linear codes and the corresponding Ramanujan graphs. Moreover, we verify that our families of Ramanujan graphs are different from the previous families in terms of eigenvalues and regularity.
Jeong et al. (Fri,) studied this question.