A survey of recent works with respect to a characterization of an (n,k,d;q)-code meeting the Griesmer bound using a min\(\cdot hyper\) in a finite projective geometry

DOI10.1016/0012-365X(89)90353-1zbMath0687.05014OpenAlexW2050004925MaRDI QIDQ1262869

Noboru Hamada, Michel Marie Deza

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0012-365x(89)90353-1

zbMATH Keywords

linear codefinite projective geometrymin\(\cdot hyper\)

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Combinatorial aspects of finite geometries (05B25) Combinatorial structures in finite projective spaces (51E20)

Related Items (7)

A geometric approach to classifying Griesmer codes ⋮ Unnamed Item ⋮ Optimal ternary linear codes ⋮ A characterization of some \(\{v_ 2+2v_ 3,v_ 1+2v_ 2;k-1,3\}\)-minihypers and some \((v_ k-30,k,3^{k-1}-21;3)\)-codes meeting the Griesmer bound ⋮ A characterization of some \([n,k,d;q\)-codes meeting the Griesmer bound using a minihyper in a finite projective geometry] ⋮ A construction of some \([n,k,d;q\)-codes meeting the Griesmer bound] ⋮ A Griesmer bound for linear codes over finite quasi-Frobenius rings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On linear codes which attain the Solomon-Stiffler bound
• Construction of optimal linear codes using flats and spreads in a finite projective geometry
• 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
• A note on the construction of optimal linear codes
• 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]
• New constructions of codes meeting the Griesmer bound
• Construction of Optimal Codes and Optimal Fractional Factorial Designs Using Linear Programming
• A new class of codes meeting the Griesmer bound
• A characterization of codes meeting the Griesmer bound
• Algebraically punctured cyclic codes
• A Bound for Error-Correcting Codes
• A note on the Griesmer bound (Corresp.)
• On a Bound Useful in the Theory of Factorial Designs and Error Correcting Codes

This page was built for publication: A survey of recent works with respect to a characterization of an (n,k,d;q)-code meeting the Griesmer bound using a min\(\cdot hyper\) in a finite projective geometry