Some Two-Weight Codes Over Chain Rings and their Strongly Regular Graphs

Irreducible cyclic codes of length \( p^2 - 1 \) $p^2-1$ are constructed as two-weight codes over a chain ring with a residue field of characteristic \( p \) $p$ . Their projective puncturings of length \( p + 1 \) $p+1$ also yield two-weight codes. Under certain conditions, these latter codes qualify as Maximum Distance Rank codes (MDR). We construct strongly regular graphs from both types of codes and compute their parameters. Additionally, we construct an infinite common cover of these graphs for a given \( p \) $p$ by extending the alphabet to \( p \) $p$ -adic numbers.