A note on difference matrices over non-cyclic finite abelian groups

Pan, Rong; Chang, Yanxun

doi:10.1016/j.disc.2015.10.028

Cited by 15 publications

(14 citation statements)

References 10 publications

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“…Thus, as immediate consequence of the main results on (H , 4, 1)-DM (see [30,50]), we have the following. There exists a homogeneous (H , 3, 1)-DM with H abelian of even order if and only if the 2-Sylow subgroup of H is not cyclic.…”

Section: Composition Constructions Via Difference Matricessupporting

confidence: 65%

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

Bonvicini

Buratti

Garonzi

et al. 2021

Des. Codes Cryptogr.

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Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems, little is known about their automorphism groups. In particular, there is no known congruence class representing the orders of a KTS with a number of automorphisms at least close to the number of points. We partially fill this gap by proving that whenever $$v \equiv 39$$ v ≡ 39 (mod 72), or $$v \equiv 4^e48 + 3$$ v ≡ 4 e 48 + 3 (mod $$4^e96$$ 4 e 96 ) and $$e \ge 0$$ e ≥ 0 , there exists a KTS on v points having at least $$v-3$$ v - 3 automorphisms. This is only one of the consequences of an investigation on the KTSs with an automorphism group G acting sharply transitively on all but three points. Our methods are all constructive and yield KTSs which in many cases inherit some of the automorphisms of G, thus increasing the total number of symmetries. To obtain these results it was necessary to introduce new types of difference families (the doubly disjoint ones) and difference matrices (the splittable ones) which we believe are interesting by themselves.

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Section: Composition Constructions Via Difference Matricessupporting

confidence: 65%

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

Bonvicini

Buratti

Garonzi

et al. 2021

Des. Codes Cryptogr.

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“…Lemma 3.1 (Pan and Chang [28]). If G is an abelian group and no cyclic, then there exists a G ( , 4, 1)-DM if and only if the 2-Sylow subgroup of G is not cyclic.…”

Section: Recursive Constructions For Rdfsmentioning

confidence: 99%

“…m n ( , ) = (6, 48): {(0, 0), (4, 44), (5,3), (3,11)}, {(0, 0), (5,28), (3,4), (4, 35)}, {(0, 0), (4, 7), (3,12), (0, 38)}, {(0, 0), (4,45), (1,17), (1,24)}, {(0, 0), (0, 5), (2,22), (0, 28)}, {(0, 0), (3,9), (1,21), (5, 30)}, {(0, 0), (5,1), (1,16), (2, 20)}, {(0, 0), (1,46), (4,5), (4, 16)}, {(0, 0), (1,40), (1,6), (2,19)}, {(0, 0), (2,46), (3,23), (4,14)}, {(0, 0), (4,43), (3,15), (3,17)}, {(0, 0), (4, 37), (0, 39), (5, 39)}, {(0, 0), (2,45), (2,<...>…”

Section: Appendix Bmentioning

confidence: 99%

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

Chen

2021

J of Combinatorial Designs

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“…When u and v are not coprime, the construction of optimal (u, v, k, λ a , λ c )-OOSPCs becomes difficult. For k = 3, 4, some results have been obtained for optimal (u, v, k, λ a , λ c )-OOSPCs [5], [6], [20], [22], [23], [19], [27], [28]. For general weight k, some results on (asymptotically ) optimal (u, v, k, λ a , λ c )-OOSPCs are also obtained [14], [21], [32].…”

Section: Introductionmentioning

confidence: 99%

“…Since gcd(p, 48)=1, then Z 2 × Z 48p is isomorphic to Z 2 × Z 48 × Z p . Let B 1 = {(0, 0, 1), (0, 0, −1), (0, 1, ), (0, 1, − )}; B 2 = {(0, 0, 0), (0, 24, ξ 2 ), (1, 0, ξ 2 + ξ), (1, 24, 2ξ 2 )}; B 3 = {(0, 0, 0), (0, 6, 1), (0, 14, 2), (1,19,3), (1,36,4)}; {(0,0),(0,13), (2,12),(2,16)}, {(0,0),(0,5), (1,19),(2,1),(2,2)}, {(0,0), (1,5), (1,15),(2,7),(2,15)}, {(0,0),(0,2), (1,13), (1,20)}.…”

mentioning

confidence: 99%

Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

Li¹,

Zhao²,

Qin³

et al. 2019

Advances in Mathematics of Communications

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Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirements. Some results had been done on optimal balanced (m, n, {3, 4}, 1)-OOSPCs. In this paper, it is proved that there exist optimal balanced (2u, 16v, {4, 5}, 1)-OOSPCs for odd integers u ≥ 1, v ≥ 1.

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A note on difference matrices over non-cyclic finite abelian groups

Cited by 15 publications

References 10 publications

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

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