Abstract
Abstract We present a unified theory of Grobner bases over a principal ideal ring with a view to applications in Coding Theory, for example to the structure of codes over a finite-chain ring, e.g. a Galois ring. Our theory is effective and yields an extension of Buchberger's algorithm to principal ideal rings. In particular, given a set of generators for a cyclic code over a Galois ring, we can compute a ‘minimal strong’ Grobner basis for the code. We give some applications to cyclic codes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
