A framework constructs new non-GRS MDS-NMDS codes from deep holes, yielding three new families while recovering prior results with lower computational complexity.
More MDS codes of non-Reed- Solomon type
6 Pith papers cite this work. Polarity classification is still indexing.
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Generalized Roth-Lempel codes yield new Hermitian self-orthogonal NMDS families and quantum NMDS codes attaining the quantum Singleton bound minus one.
Constructs and characterizes MDS/NMDS modified GRS and extended GRS codes with flexible Euclidean and Hermitian hull dimensions and lengths.
A cyclotomic field reduction method constructs non-RS cyclic MDS codes over finite fields by converting MDS verification to characteristic-zero minor checks, producing codes with flexible parameters.
Two new families of linear codes are built from modified GRS generator matrices, producing non-GRS MDS codes with derived parity-check matrices and self-duality conditions.
Extended TGRS codes are built by adding three columns to TGRS generator matrices; conditions for MDS/AMDS/NMDS are derived and non-GRS nature is shown via Schur product.
citing papers explorer
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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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Generalized Roth--Lempel Codes: NMDS Characterization, Hermitian Self-Orthogonality, and Quantum Constructions
Generalized Roth-Lempel codes yield new Hermitian self-orthogonal NMDS families and quantum NMDS codes attaining the quantum Singleton bound minus one.
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The MDS or NMDS for Modified GRS codes with flexible hull dimensions and lengths
Constructs and characterizes MDS/NMDS modified GRS and extended GRS codes with flexible Euclidean and Hermitian hull dimensions and lengths.
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Non-RS type cyclic MDS codes over finite fields via cyclotomic field reduction
A cyclotomic field reduction method constructs non-RS cyclic MDS codes over finite fields by converting MDS verification to characteristic-zero minor checks, producing codes with flexible parameters.
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Two Families of Linear Codes Containing Non-GRS MDS Codes
Two new families of linear codes are built from modified GRS generator matrices, producing non-GRS MDS codes with derived parity-check matrices and self-duality conditions.
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MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes
Extended TGRS codes are built by adding three columns to TGRS generator matrices; conditions for MDS/AMDS/NMDS are derived and non-GRS nature is shown via Schur product.