Tight 2-designs and perfect 1-codes in Doob graphs

DOI10.1016/S0378-3758(99)00126-3zbMath0974.05011OpenAlexW2008192074WikidataQ127185659 ScholiaQ127185659MaRDI QIDQ1569871

Akihiro Munemasa, Jack H. Koolen

Publication date: 13 September 2001

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-3758(99)00126-3

zbMATH Keywords

distance-regular graphsHamming graphsDoob graphsperfect 1-codestight 2-designs

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Association schemes, strongly regular graphs (05E30) Other types of codes (94B60)

Related Items (5)

Perfect codes in Doob graphs ⋮ On the minimum supports of some eigenfunctions in the Doob graphs ⋮ Additive perfect codes in Doob graphs ⋮ On graphs with smallest eigenvalue at least \(-3\) and their lattices ⋮ Steiner systems \(S(2, 4, \frac{3^m-1}{2})\) and 2-designs from ternary linear codes of length \(\frac{3^m-1}{2}\)

Uses Software

• GAP
• GRAPE

Cites Work

• On the nonexistence of nontrivial perfect e-codes and tight 2e-designs in Hamming schemes H(n,q) with e\(\geq 3\) and q\(\geq 3\)
• Perfect codes in graphs
• The Uniqueness of the $\mathrm{L}_2$ Association Scheme
• On the Zeros of the Askey–Wilson Polynomials, with Applications to Coding Theory
• On Orthogonal Arrays of Strength 4 Achieving Rao's Bound
• Four fundamental parameters of a code and their combinatorial significance
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