New bounds for \(n_{4}(k,d)\) and classification of some optimal codes over GF(4)

DOI10.1016/j.disc.2003.11.003zbMath1054.94021OpenAlexW2067373633MaRDI QIDQ1827695

Markus Grassl, Zlatko G. Varbanov, Iliya G. Bouyukliev

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.disc.2003.11.003

zbMATH Keywords

Griesmer boundquaternary linear codesoptimal codes

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Bounds on codes (94B65) Linear codes and caps in Galois spaces (51E22)

Related Items (5)

Nonexistence of some linear codes over the field of order four ⋮ Optimal quaternary linear codes with one-dimensional Hermitian hull and related EAQECCs ⋮ On optimal non-projective ternary linear codes ⋮ Maximal entanglement entanglement-assisted quantum codes constructed from linear codes ⋮ On optimal linear codes over \(\mathbb F_5\)

Uses Software

• Magma
• Code Tables

Cites Work

• Minimum block length of a linear q-ary code with specified dimension and code distance
• Codes and projective multisets
• The nonexistence of some optimal ternary codes of dimension five
• 41 is the largest size of a cap in \(PG(4, 4)\)
• On the minimum length of quaternary linear codes of dimension five
• Optimal linear codes over \(\mathrm{GF}(4)\)
• The correspondence between projective codes and 2-weight codes
• The Magma algebra system. I: The user language
• Classifying subspaces of Hamming spaces
• On the nonexistence of quaternary \([51, 4, 37\) codes]
• Optimum codes of dimension 3 and 4 over GF(4)
• Using combinatorial optimization to design good unit-memory convolutional codes
• Improved bounds for ternary linear codes of dimension 7
• The smallest length of eight-dimensional binary linear codes with prescribed minimum distance
• Some new results for optimal ternary linear codes
• The nonexistence of some five-dimensional quaternary linear codes
• Optimal quaternary linear codes of dimension five
• Algebraically punctured cyclic codes
• A Bound for Error-Correcting Codes
• A note on the Griesmer bound (Corresp.)
• The nonexistence of some quaternary linear codes of dimension 5
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