Starters and related codes

Chen, K.; Ge, G.; Zhu, L.

doi:10.1016/s0378-3758(99)00119-6

Cited by 83 publications

(90 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From Lemma 1.5, the necessary conditions for the existence of a GS 4 Proof. Let v 4t 1 and $ be a primitive element of GFv.…”

Section: Rgdd Construction For Small Hgsmentioning

confidence: 99%

“…There exists a 4-GDD12 4 with the property that each group can be partitioned into two subgroups of size 6 and its blocks can be partitioned into two sets T 0 , T 1 such that the minimum distance of either T 0 Y or T 1 is 4 with respect to the subgroups.…”

Section: Lemma 74 There Exists a 4-gdd6mentioning

confidence: 99%

“…Much work has been done for the existence of GStY kY vY g when t 2 and k 3 (see [7,2,13,12,3,4,15]). However, not much is known for other cases.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Steiner systems GS₄ (2, 4, v, g) for g = 2, 3, 6

Wu¹,

Ge²,

Zhu³

2001

J of Combinatorial Designs

Self Cite

View full text Add to dashboard Cite

Generalized Steiner systems GS d tY kY vY g were ®rst introduced by Etzion and used to construct optimal constant-weight codes over an alphabet of size g 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS2Y 3Y vY g. However, for block size four there is not much known on GS d 2Y 4Y vY g. In this paper, the necessary conditions for the existence of a GS d tY kY vY g are given, which answers an open problem of Etzion. Some singular indirect product constructions for GS d 2Y kY vY g are also presented. By using both recursive and direct constructions, it is proved that the necessary conditions for the existence of a GS 4 2Y 4Y vY g are also suf®cient for g

show abstract

“…From Lemma 1.5, the necessary conditions for the existence of a GS 4 Proof. Let v 4t 1 and $ be a primitive element of GFv.…”

Section: Rgdd Construction For Small Hgsmentioning

confidence: 99%

Section: Lemma 74 There Exists a 4-gdd6mentioning

confidence: 99%

See 1 more Smart Citation

Generalized Steiner systems GS₄ (2, 4, v, g) for g = 2, 3, 6

Wu¹,

Ge²,

Zhu³

2001

J of Combinatorial Designs

Self Cite

View full text Add to dashboard Cite

show abstract

“…Starters were first used by Stanton and Mullin to construct Room squares [1]. Since then, starters have been widely used in several combinatorial designs such as Room cubes [2], Howell designs [3,4], Kirkman triple systems [5], Kirkman squares and cubes [6,7], Kotzig factorizations [8,9], Hamilton path tournament designs [10], and optimal optical orthogonal codes [11]. A starter sequence of order is an integer sequence; = ( 1 , 2 , .…”

Section: Introductionmentioning

confidence: 99%

Starter Labelling of k-Windmill Graphs with Small Defects

Omer

Shalaby

2015

International Journal of Combinatorics

View full text Add to dashboard Cite

A graph on 2 vertices can be starter-labelled, if the vertices can be given labels from the nonzero elements of the additive group Z 2 +1 such that each label , either or −1 , is assigned to exactly two vertices and the two vertices are separated by either edges or −1 edges, respectively. Mendelsohn and Shalaby have introduced Skolem-labelled graphs and determined the conditions ofwindmills to be Skolem-labelled. In this paper, we introduce starter-labelled graphs and obtain necessary and sufficient conditions for starter and minimum hooked starter labelling of all -windmills.

show abstract

“…1. The existence of a GS(2, 3, n, g) has been solved also for g 6 in [4] and for g 7, 8 in [12] by different methods.…”

mentioning

confidence: 99%