MDS and Self-dual Codes over Rings
Kenza Guenda, T. Aaron Gulliver
TL;DR
This paper explores the structure of constacyclic codes over various rings and establishes conditions for the existence of MDS codes, enabling the construction of infinite families of MDS self-dual codes over different ring types.
Contribution
It provides new structural insights into constacyclic codes over rings and characterizes when MDS codes exist over principal ideal rings, facilitating their construction.
Findings
Characterization of constacyclic codes over rings
Necessary and sufficient conditions for MDS codes over principal ideal rings
Construction of infinite families of MDS self-dual codes
Abstract
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.
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