Polyadic Constacyclic Codes
Bocong Chen, Hai Q. Dinh, Yun Fan, San Ling
TL;DR
This paper establishes conditions for the existence and multipliers of Type I m-adic constacyclic codes and constructs optimal codes like Reed-Solomon and MDS codes from them.
Contribution
It provides necessary and sufficient conditions for Type I m-adic constacyclic codes and their multipliers, and constructs optimal codes including generalized Reed-Solomon and MDS codes.
Findings
Conditions for existence of Type I m-adic constacyclic codes
Conditions for s to be a multiplier of such codes
Construction of optimal codes from these codes
Abstract
For any given positive integer , a necessary and sufficient condition for the existence of Type I -adic constacyclic codes is given. Further, for any given integer , a necessary and sufficient condition for to be a multiplier of a Type I polyadic constacyclic code is given. As an application, some optimal codes from Type I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant MDS codes, are constructed.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · graph theory and CDMA systems