Perfect 1-error-correcting Hurwitz weight codes

Abstract

Let $\pi$ be a Hurwitz prime and $p = \pi \pi ^\star$. In this paper, we construct perfect 1-error-correcting codes in $\cal{H}_{\pi}^n$ for every prime number $p > 3$, where $\cal{H}$ denotes the set of Hurwitz integers.