Steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m+ 1 over $$\mathbb{F}_2$$

Zinoviev, V. A.; Zinoviev, Dmitrii

doi:10.1134/s0032946012020020

Cited by 19 publications

(38 citation statements)

References 9 publications

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“…It is known (see [7,8]) that in the case v = 15, there exist 864 Steiner triple systems of rank 11, 18 144 triple Systems of rank 12 and 105 408 triple systems of rank 13, orthogonal to the code generated by the matrix  1111 1111 0000 000 1111 0000 1111 000  .…”

Section: Comparison To the Known Resultsmentioning

confidence: 98%

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On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
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4
0
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Section: Comparison To the Known Resultsmentioning

confidence: 98%

“…The case of rank 2 m − m + 1 has been considered in [7]. In that paper all different Steiner triple systems STS(v) of this rank were enumerated and the exact number of different triple systems was obtained [8].…”

Section: Introductionmentioning

confidence: 99%

On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
1
4
0
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“…The equation V (1) |ξ = 0 amounts to the relations 18) which should be considered on space of |ξ (8.38). Using (F.18), we find that the equation V (0) |ξ = 0 amounts to the relations…”

Section: Appendix a Counting Of On-shell Dof For Spin-1 Fieldmentioning

confidence: 99%

Ordinary-derivative formulation of conformal low-spin fields

Metsaev

2012

J. High Energ. Phys.

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Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0, 1, 2 conformal bosonic fields and first-derivative formulation for spin 1/2, 3/2 conformal fermionic fields are developed. For the spin 1, 3/2, 2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field. With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term. Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries. Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories. *

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“…The dimensions of these codes agree with the formula 2m 2 + 1. (C(m, 3))) 2 [9,5,4] [9, 9, 1] 3 [27,7,15] [27, 19, 6] 4 [81, 9,48] [81, 33, 21]…”

Section: Codes Of Designs Held In a Class Of Affine-invariant Ternarymentioning

confidence: 99%

Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes

Ding

Tang

Tonchev

2019

Des. Codes Cryptogr.

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In this paper, the 3-rank of the incidence matrices of 2-designs supported by the minimum weight codewords in a family of ternary linear codes considered in [C. Ding, C. Li, Infinite families of 2-designs and 3-designs from linear codes, Discrete Mathematics 340(10) (2017) 2415-2431] are computed. A lower bound on the minimum distance of the ternary codes spanned by the incidence matrices of these designs is derived, and it is proved that the codes are subcodes of the 4th order generalized Reed-Muller codes.

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Steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m+ 1 over $$\mathbb{F}_2$$

Cited by 19 publications

References 9 publications

On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
1
4
0
View full text Add to dashboard Cite

On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
1
4
0
View full text Add to dashboard Cite

Ordinary-derivative formulation of conformal low-spin fields

Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes

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Steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m+ 1 over $$\mathbb{F}_2$$

Cited by 19 publications

References 9 publications

On the number of Steiner triple systems S(2m−1,3,2) of rank Zinoviev1 2016Discrete Mathematics8140View full textAdd to dashboardCite

On the number of Steiner triple systems S(2m−1,3,2) of rank Zinoviev1 2016Discrete Mathematics8140View full textAdd to dashboardCite

Ordinary-derivative formulation of conformal low-spin fields

Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes

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Product

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On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
1
4
0
View full text Add to dashboard Cite

On the number of Steiner triple systems S(2m−1,3,2) of rank
Zinoviev
¹

2016
Discrete Mathematics
8
1
4
0
View full text Add to dashboard Cite