On Cyclic Codes in Incidence Rings
journal contribution
posted on 2023-05-16, 17:52 authored by Alfaro, R, Kelarev, AVCyclic codes are defined as ideals in polynomial quotient rings. We are using a matrix ring construction in a similar way to define classes of codes. It is shown that all cyclic and all linear codes can be embedded as ideals in this construction. A formula for the largest Hamming weight of one-sided ideals in incidence rings is given. It is shown that every incidence ring defined by a directed graph always possesses a principal one-sided ideal that achieves the optimum Hamming weight. © 2006 Akadémiai Kiadó, Budapest.
Funding
Australian Research Council
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Publication title
Studia Scientiarum Mathematicarum HungaricaVolume
43Pagination
69-77ISSN
0081-6906Department/School
School of Information and Communication TechnologyPublisher
Hungarian Academy of SciencesPlace of publication
Budapest, HungaryRepository Status
- Restricted
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