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(Z)(n)(pi), are constructed for every prime number p equivalent to 1(mod 4). This completes a result of the authors in an earlier work, Perfect Mannheim, Lipschitz and Hurwitz weight codes, (Math. Commun. 19(2014), 253-276), where a construction is given in the case p 3 (mod 4).