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MDS and MHDR cyclic codes over finite chain rings (2303.15819v1)
Published 28 Mar 2023 in cs.IT and math.IT
Abstract: In this work, a unique set of generators for a cyclic code over a finite chain ring has been established. The minimal spanning set and rank of the code have also been determined. Further, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code have been obtained. Some examples of optimal cyclic codes have also been presented.