A proof of the Etzion-Silberstein conjecture for monotone and MDS-constructible Ferrers diagrams

DOI10.1016/j.jcta.2024.105937MaRDI QIDQ6612125

Alessandro Neri, Mima Stanojkovski

Publication date: 30 September 2024

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

zbMATH Keywords

Ferrers diagramsrank-metric codesconvex diagramsEtzion-Silberstein conjectureMDS-constructible diagramsmonotone diagrams

Mathematics Subject Classification ID

Theory of error-correcting codes and error-detecting codes (94Bxx) Basic linear algebra (15Axx) Finite fields and commutative rings (number-theoretic aspects) (11Txx)

Cites Work

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• Linear subspaces of matrices associated to a Ferrers diagram and with a prescribed lower bound for their rank
• Galois extensions and subspaces of alternating bilinear forms with special rank properties
• Theory of codes with maximum rank distance
• Bilinear forms over a finite field, with applications to coding theory
• Invertible preservers and algebraic groups
• Several classes of optimal Ferrers diagram rank-metric codes
• Optimal Ferrers Diagram Rank-Metric Codes
• A Rank-Metric Approach to Error Control in Random Network Coding
• Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams
• Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations
• Constructions for Optimal Ferrers Diagram Rank-Metric Codes
• Subspace codes from Ferrers diagrams
• Partial-MDS Codes and Their Application to RAID Type of Architectures
• Maximum-rank array codes and their application to crisscross error correction
• Rook Theory of the Etzion-Silberstein Conjecture

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