Steiner triple systems \(S(2^m-1,3,2)\) of rank \(2^m-m+1\) over \(\mathbb F_2\)

DOI10.1134/S0032946012020020zbMath1274.05045OpenAlexW1979174700MaRDI QIDQ375950

Dmitrii Zinoviev, Victor A. Zinoviev

Publication date: 1 November 2013

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

Full work available at URL: https://doi.org/10.1134/s0032946012020020

Mathematics Subject Classification ID

Triple systems (05B07)

Related Items (6)

On the number of Steiner triple systems \(S(2^m - 1, 3, 2)\) of rank \(2^m - m + 2\) over \(\mathbb{F}_2\) ⋮ Counting Steiner triple systems with classical parameters and prescribed rank ⋮ The number of the non-full-rank Steiner quadruple systems \(S ( v , 4 , 3 )\) ⋮ On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements ⋮ The projective general linear group \(\mathrm{PGL}(2,2^m)\) and linear codes of length \(2^m+1\) ⋮ Linear codes of 2-designs associated with subcodes of the ternary generalized Reed-Muller codes

Cites Work

• On resolvability of Steiner systems \(S ( v = 2^{ m }, 4, 3)\) of rank \(r \leq v - m + 1\) over \(\mathbb{F}_{2}\)
• Ranks of incidence matrices of Steiner triple systems
• Steiner quadruple systems - a survey
• Codes of Steiner triple and quadruple systems
• On 2-ranks of Steiner triple systems
• Nonisomorphic Steiner triple systems
• Classification of Steiner quadruple systems of order 16 and rank at most 13
• On Quadruple Systems
• A General Product Construction for Error Correcting Codes
• A formula for the number of Steiner quadruple systems on 2ⁿ points of 2‐rank 2ⁿ−n
• A mass formula for Steiner triple systems STS\((2^n-1)\) of 2-rank \(2^n-n\)
• Unnamed Item

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