Designs from pairs of finite fields. A cyclic unital U(6) and other regular steiner 2-designs

Bagchi, Sanjib; Bagchi, Bhaskar

doi:10.1016/0097-3165(89)90061-7

Cited by 36 publications

(48 citation statements)

References 6 publications

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“…The group of multipliers of E is {1, 3, 9} which is also a group of multipliers of the matrix A. Thus, according to Theorem 3.13, {(1, 1), (1,3), (1,9)} is a group of multipliers of F. Using the isomorphism ψ: Proof. We have G = ⊕ q∈Q C q where Q is the multiset of elementary divisors of G. Hence, if we prove the existence of a (q, k, λ)-DF and a (q, k, 1)-DM for each q ∈ Q, the required (G, k, λ)-DF could be obtained using recursively Theorem 3.10.…”

Section: Then the Familymentioning

confidence: 95%

Recursive constructions for difference matrices and relative difference families

1998

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We present a new recursive construction for difference matrices whose application allows us to improve some results by D. Jungnickel. For instance, we prove that for any Abelian p‐group G of type (n1, n2, …, nt) there exists a (G, pe, 1) difference matrix with e = ${\lfloor}{\Sigma _i n_i\over\max _i n_i}{\rfloor}.$ Also, we prove that for any group G there exists a (G, p, 1) difference matrix where p is the smallest prime dividing |G|. Difference matrices are then used for constructing, recursively, relative difference families. We revisit some constructions by M. J. Colbourn, C. J. Colbourn, D. Jungnickel, K. T. Phelps, and R. M. Wilson. Combining them we get, in particular, the existence of a multiplier (G, k, λ)‐DF for any Abelian group G of nonsquare‐free order, whenever there exists a (p, k, λ)‐DF for each prime p dividing |G|. Then we focus our attention on a recent construction by M. Jimbo. We improve this construction and prove, as a corollary, the existence of a (G, k, λ)‐DF for any group G under the same conditions as above. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 165–182, 1998

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Section: Then the Familymentioning

confidence: 95%

Recursive constructions for difference matrices and relative difference families

1998

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“…Since the desarguesian projective planes of square order admit unitary polarities, unitals exist for each prime-power q (these are the classical or hermitian unitals). Unitals also exist for q = 6, see [1,18].…”

Section: Some New Unitals (65 5 1)mentioning

confidence: 98%

The Kramer-Mesner method with tactical decompositions: some new unitals on 65 points

2011

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“…All known unitals with parameters (m 3 + 1, m + 1, 1) have m equal to a prime power, except for one example with m = 6 constructed by Mathon [9], and independently by Bagchi and Bagchi [3]. In this note, we will only consider unitals embedded in PG(2, q 2 ), i.e., unitals coming from a set of q 3 + 1 points of PG(2, q 2 ) which meets every line of PG(2, q 2 ) in either 1 or q + 1 points.…”

Section: Introductionmentioning

confidence: 99%

On the dimensions of the binary codes of a class of unitals

Leung

Xiang

2009

Discrete Mathematics

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a b s t r a c tLet U β be the special Buekenhout-Metz unital in PG(2, q 2 ), formed by a union of q conics, where q = p e is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design U β is less than or equal to q 3 + 1 − q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q 3 (1 − 1 p ) + q 2 p .

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Designs from pairs of finite fields. A cyclic unital U(6) and other regular steiner 2-designs

Cited by 36 publications

References 6 publications

Recursive constructions for difference matrices and relative difference families

Recursive constructions for difference matrices and relative difference families

The Kramer-Mesner method with tactical decompositions: some new unitals on 65 points

On the dimensions of the binary codes of a class of unitals

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