(1) Department of Mathematics, National University of Singapore, Singapore, 117543;(2) CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia Antipolis, France
Abstract:
The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech lattice is derived.