New MDS codes of non-GRS type and NMDS codes
Yujie Zhi, Shixin Zhu
TL;DR
This paper introduces new classes of MDS and NMDS codes that are not equivalent to GRS codes, providing algebraic conditions and employing the Schur method to establish their uniqueness and properties.
Contribution
It establishes necessary and sufficient conditions for certain linear codes to be MDS or NMDS and demonstrates their non-equivalence to GRS codes using the Schur method.
Findings
Identified new classes of MDS and NMDS codes
Established algebraic conditions for these codes
Proved non-equivalence to GRS codes using the Schur method
Abstract
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes.
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Taxonomy
TopicsDistributed and Parallel Computing Systems · Environmental Monitoring and Data Management