Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.
Bibliographical notePublisher Copyright:
© 1963-2012 IEEE.
- Crossed products
- Hamming isometry
- completion property
- skew-constacyclic codes
- twisted elementary Abelian codes
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences