A framework constructs new non-GRS MDS-NMDS codes from deep holes, yielding three new families while recovering prior results with lower computational complexity.
The (+)-extended twisted generalized Reed-Solomon code
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Column twisted Reed-Solomon codes are shown to be MDS under sufficient conditions, with Schur square dimension 2k implying they are not equivalent to Reed-Solomon codes, and support lengths up to (q+3)/2 for large odd prime power q.
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A framework for constructing non-GRS MDS-NMDS codes from deep holes and its application
A framework constructs new non-GRS MDS-NMDS codes from deep holes, yielding three new families while recovering prior results with lower computational complexity.
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Column Twisted Reed-Solomon Codes as MDS Codes
Column twisted Reed-Solomon codes are shown to be MDS under sufficient conditions, with Schur square dimension 2k implying they are not equivalent to Reed-Solomon codes, and support lengths up to (q+3)/2 for large odd prime power q.