A characterization of \(\{ 2\upsilon{}_{\alpha{}+1}+2\upsilon{}_{\beta{}+1},2\upsilon_ \alpha{}+2\upsilon{}_ \beta{} ;t,q\}\)-minihypers in PG\((t,q)(t\geq 2,q\geq 5\) and \(0\leq\alpha{}<\beta{}

DOI10.1016/0012-365X(91)90214-MzbMath0746.51015OpenAlexW2027167819MaRDI QIDQ1182872

Noboru Hamada, Michel Marie Deza

Publication date: 28 June 1992

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(91)90214-m

zbMATH Keywords

projective spaceGriesmer boundlinear codeminihyper

Mathematics Subject Classification ID

Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial structures in finite projective spaces (51E20)

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Cites Work

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• On linear codes which attain the Solomon-Stiffler bound
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• Characterization of \(\{(q+1)+2,1;t,q\}-\min \cdot hypers\) and \(\{2(q+1)+2,2;2,q\}-\min \cdot hypers\) in a finite projective geometry
• Characterization of \(\{v_{\mu +1}+2v_{\mu},v_{\mu}+2v_{\mu - 1};t,q\}\)-min\(\cdot hypers\) and its applications to error-correcting codes
• Characterization of \(\{2(q+1)+2,2;t,q\}\)-\(\min \cdot hypers\) in PG(t,q) (t\(\geq 3,q\geq 5)\) and its applications to error-correcting codes
• A characterization of \(\{v_{\mu +1}+\epsilon,v_{\mu};t,q\}\)-min\(\cdot hypers\) and its applications to error-correcting codes and factorial designs
• On a geometrical method of construction of maximal t-linearly independent sets
• A characterization of some \([n,k,d;q\)-codes meeting the Griesmer bound using a minihyper in a finite projective geometry]
• On the uniqueness resp. Nonexistence of certain codes meeting the Griesmer bound
• Construction of Optimal Codes and Optimal Fractional Factorial Designs Using Linear Programming
• A characterization of codes meeting the Griesmer bound
• Algebraically punctured cyclic codes
• A Bound for Error-Correcting Codes

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