On resolvability of Steiner systems \(S ( v = 2^{ m }, 4, 3)\) of rank \(r \leq v - m + 1\) over \(\mathbb{F}_{2}\)

DOI10.1134/S003294600701005XzbMath1236.05036MaRDI QIDQ415706

Victor A. Zinoviev, Dmitrii Zinoviev

Publication date: 9 May 2012

Published in: Problems of Information Transmission (Search for Journal in Brave)

zbMATH Keywords

rankSteiner systemconstructionSteiner quadrupe system

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Steiner systems in finite geometry (51E10) Triple systems (05B07)

Related Items (5)

Generalized Preparata codes and 2-resolvable Steiner quadruple systems ⋮ The number of the non-full-rank Steiner quadruple systems \(S ( v , 4 , 3 )\) ⋮ Steiner triple systems \(S(2^m-1,3,2)\) of rank \(2^m-m+1\) over \(\mathbb F_2\) ⋮ Non-full-rank Steiner quadruple systems \(S(v,4,3)\) ⋮ On one transformation of Steiner quadruple systems \(S(\upsilon , 4, 3)\)

Cites Work

• Classification of Steiner quadruple systems of order 16 and rank 14
• The Steiner quadruple systems of order 16
• The existence of resolvable Steiner quadruple systems
• On projective and affine hyperplanes
• Ranks of incidence matrices of Steiner triple systems
• Steiner quadruple systems - a survey
• On 2-ranks of Steiner triple systems
• Vasil'ev codes of length \(n=2^m\) and doubling of Steiner systems \(S(n,4,3)\) of a given rank
• Classification of Steiner quadruple systems of order 16 and rank at most 13
• On Quadruple Systems
• A formula for the number of Steiner quadruple systems on 2ⁿ points of 2‐rank 2ⁿ−n
• Resolvable Steiner Quadruple Systems for the Last 23 Orders
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