Constacyclic Codes Over Finite Principal Ideal Rings
Aicha Batoul, Kenza Guenda, T. Aaron Gulliver
TL;DR
This paper explores the structure of constacyclic codes over finite principal ideal rings, establishing an isomorphism with cyclic codes and providing conditions for the existence of self-dual codes.
Contribution
It introduces a key isomorphism between constacyclic and cyclic codes over finite principal ideal rings and characterizes when self-dual codes exist.
Findings
Established an isomorphism between constacyclic and cyclic codes
Derived necessary and sufficient conditions for self-dual codes
Enhanced understanding of code structures over principal ideal rings
Abstract
In this paper, we give an important isomorphism between contacyclic codes and cyclic codes over finite principal ideal rings. Necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite principal ideal rings are given.
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