Two weight ${\mathbb{Z}}_{p^k}$-codes, $p$ odd prime

Abstract

We show that regular homogeneous two-weight ${\mathbb{Z}}_{p^k}$-codes where $p$ is odd and $k⩾2$ with dual Hamming distance at least four do not exist. The proof relies on existence conditions for the strongly regular graph built on the cosets of the dual code.

This paper has been submitted in early 2016