Infinite series of 3-designs in the extended quadratic residue code

DOI10.1002/JCD.21950zbMATH Open1548.05043MaRDI QIDQ6615597

Madoka Awada

Publication date: 8 October 2024

Published in: Journal of Combinatorial Designs (Search for Journal in Brave)

zbMATH Keywords

\(t\)-designJacobi polynomialextended quadratic residue codeharmonic weight enumerator

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Linear codes (general theory) (94B05)

Cites Work

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• The lengths of Hermitian self-dual extended duadic codes
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• Simple 3-designs and PSL\((2,q )\) with \(q \equiv 1\pmod4\)
• Harmonic weight enumerators of nonbinary codes and MacWilliams identities
• Lattices and Codes
• The Gleason-Prange theorem
• On the notion of Jacobi polynomials for codes
• Fundamentals of Error-Correcting Codes
• The automorphism groups of the generalized quadratic residue codes
• Designs from Linear Codes
• New 5-designs
• A new proof of the Assmus-Mattson theorem for non-binary codes
• Exceptional designs in some extended quadratic residue codes
• A note on \(t\)-designs in isodual codes
• The extended binary quadratic residue code of length 42 holds a 3-design

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