On near-MDS codes and caps

DOI10.1007/s10623-022-01141-0OpenAlexW4308933491MaRDI QIDQ2692969

Michela Ceria, Giuseppe Marino, Francesco Pavese, Antonio Cossidente

Publication date: 17 March 2023

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.03402

zbMATH Keywords

capovoidnear-MDS codetwisted cubic

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Linear codes and caps in Galois spaces (51E22) Combinatorial structures in finite projective spaces (51E20)

Uses Software

• Magma

Cites Work

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• On the completeness of plane cubic curves over finite fields
• Near-MDS codes from elliptic curves
• The Magma algebra system. I: The user language
• Ovoids of parabolic spaces
• A family of caps in projective 4-space in odd characteristic
• Intersection pattern of the classical ovoids in symplectic 3-space of even order
• Caps of order 3\(q^{2}\) in affine 4-space in characteristic 2
• On the extendibility of near-MDS elliptic codes
• On near-MDS codes
• Near-MDS codes arising from algebraic curves
• Near MDS codes from oval polynomials
• The geometry of covering codes: small complete caps and saturating sets in Galois spaces
• Linear codes with covering radius 2 and other new covering codes
• General Galois Geometries
• Ovoids of PG(3,q ), q Even, with a Conic Section

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