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<p>We present a construction method for Ramanujan graphs from simplicial complexes with one or two <i>blockers</i>, using the corresponding multivariable functions, where <i>blockers</i> 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.</p>

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Ramanujan graphs from simplicial complexes with few blockers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月16日

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  • Jihye Jeong,
  • Jong Yoon Hyun,
  • Yoonjin Lee

摘要

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.