On the nonexistence of nontrivial perfect e-codes and tight 2e-designs in Hamming schemes H(n,q) with e\(\geq 3\) and q\(\geq 3\)

DOI10.1007/BF01788088zbMath0595.94009MaRDI QIDQ1078149

Yiming Hong

Publication date: 1986

Published in: Graphs and Combinatorics (Search for Journal in Brave)

zbMATH Keywords

nonexistence of designs in Hamming schemesnonexistence of perfect codes

Mathematics Subject Classification ID

Other designs, configurations (05B30) Combinatorial codes (94B25)

Related Items (8)

More zeros of Krawtchouk polynomials ⋮ Distance-regular graphs of Hamming type ⋮ On the existence of saturated and nearly saturated asymmetrical orthogonal arrays ⋮ On tight 4-designs in Hamming association schemes ⋮ Integer zeros of \(q\)-Krawtchouk polynomials in classical combinatorics ⋮ Tight 2-designs and perfect 1-codes in Doob graphs ⋮ On balanced orthogonal multi-arrays: Existence, construction and application to design of experiments ⋮ On existence of two symbol complete orthogonal arrays

Cites Work

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• On the nonexistence of unknown perfect 6- and 8-codes in Hamming schemes H(n,q) with q arbitrary
• An improved version of Lloyd's theorem
• On perfect codes in the Hamming schemes H(n,q) with q arbitrary
• Nonexistence of nontrivial perfect codes in case \(q=p^r_1p^s_2\), \(e\geq 3\)
• Two theorems on perfect codes
• Perfect codes in graphs
• On the Zeros of the Askey–Wilson Polynomials, with Applications to Coding Theory
• On Orthogonal Arrays of Strength 4 Achieving Rao's Bound

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