Some constructions of non-generalized Reed-Solomon MDS Codes
Kanat Abdukhalikov, Cunsheng Ding, Gyanendra K. Verma
TL;DR
This paper explores specific extended codes related to Reed-Solomon codes, establishing conditions for their non-GRS MDS status, and offers new insights into their structure through finite projective space connections.
Contribution
It provides necessary and sufficient conditions for certain extended codes to be non-GRS MDS codes and introduces a new characterization of o-monomials via projective geometry.
Findings
Identified conditions for non-GRS MDS codes
Determined parity check matrices for these codes
Connected MDS codes with arcs in finite projective spaces
Abstract
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs in finite projective spaces, we give a new characterization of o-monomials.
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Taxonomy
TopicsCoding theory and cryptography · Quantum Computing Algorithms and Architecture · graph theory and CDMA systems