Abstract
In this paper, it is shown that some results in the theory of rank-metric codes over finite fields can be extended to finite commutative principal ideal rings. More precisely, the rank metric is generalized and the rank-metric Singleton bound is established. The definition of Gabidulin codes is extended and it is shown that its properties are preserved. The theory of Gröbner bases is used to give the unique decoding, minimal list decoding, and error-erasure decoding algorithms of interleaved Gabidulin codes. These results are then applied in space-time codes and in random linear network coding as in the case of finite fields. Specifically, two existing encoding schemes of random linear network coding are combined to improve the error correction.
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.
