Some Irreducible Codes Invariant under the Janko Group, $J_1$ or $J_2$

Abstract

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.