Some Irreducible Codes Invariant under the Janko Group, \(J_{1}\) or \(J_{2}\)

A construction of graphs, codes, and designs acted on by simple primitive groups described in [9, 10] is used to find some self-orthogonal, irreducible, and indecomposable codes acted on by one of the simple Janko groups, \( J_1 \) or \( J_2 \). In particular, most of the irreducible modules over the fields \( \mathbb{F}_p \) for \( p \in \{2, 3, 5, 7, 11, 19\} \) for \( J_1 \), and \( p \in \{2, 3, 5, 7\} \) for \( J_2 \), can be represented in this way as linear codes invariant under the groups.