Perfect 1-error-correcting Lipschitz weight codes

Abstract

Let $\pi$ be a Lipschitz prime and $p=\pi\pi^\star$. Perfect 1-error-correcting codes in $H(\mathbb{Z})_\pi^n$ are constructed for every prime number $p\equiv1(\bmod\;4)$. This completes a result of the authors in an earlier work, \emph{Perfect Mannheim, Lipschitz and Hurwitz weight codes},  (Mathematical Communications, Vol 19, No 2, pp. 253 -- 276 (2014)), where a construction is given in the case $p\equiv3\,(\bmod\;4)$.