  A $k$-uniform hypergraph is a hypergraph where each $k$-hyperedge has exactly
$k$ vertices. A $k$-homogeneous access structure is represented by a
$k$-uniform hypergraph $\mathcal{H}$, in which the participants correspond to
the vertices of hypergraph $\mathcal{H}$. A set of vertices can reconstruct the
secret value from their shares if they are connected by a $k$-hyperedge, while
a set of non-adjacent vertices does not obtain any information about the
secret. One parameter for measuring the efficiency of a secret sharing scheme
is the information rate, defined as the ratio between the length of the secret
and the maximum length of the shares given to the participants. Secret sharing
schemes with an information rate equal to one are called ideal secret sharing
schemes. An access structure is considered ideal if an ideal secret sharing
scheme can realize it. Characterizing ideal access structures is one of the
important problems in secret sharing schemes. The characterization of ideal
access structures has been studied by many authors~\cite{BD, CT,JZB,
FP1,FP2,DS1,TD}. In this paper, we characterize ideal $k$-homogeneous access
structures using the independent sequence method. In particular, we prove that
the reduced access structure of $\Gamma$ is an $(k, n)$-threshold access
structure when the optimal information rate of $\Gamma$ is larger than
$\frac{k-1}{k}$, where $\Gamma$ is a $k$-homogeneous access structure
satisfying specific criteria.
