Constructions of optimal optical orthogonal codes with weight five

Abstract

Several direct constructions via skew starters and Weil's theorem on character sum estimates are given in this paper for optimal ðgv v; 5; 1Þ optical orthogonal codes (OOCs) where 60 g 180 satisfying g 0 ðmod 20Þ and v v is a product of primes greater than 5. These improve the known existence results on optimal OOCs. Especially, we provide an optimal ðv v; 5; 1Þ-OOC for any integer v

New results on optimal (v, 4, 2, 1) optical orthogonal codes

“…Optical orthogonal codes have great importance in the applications [19] and for a long time the ones most investigated have been the optimal (v, k, 1)-OOCs [9,18] with special attention to those that are difference families [1,8,13,15,16,26] or relative difference families [11,14,21] in view of their importance in design theory [2,5,6,10]. In the last years several interesting results have also been obtained about optimal (v, k, λ)-OOCs with λ = 2 [3,17,20] and even with λ > 2 [4].…”

On constructions for optimal two-dimensional optical orthogonal codes

“…As indicated in [5,47], 1-D OOCs are closely related to combinatorial designs. Many 1-D OOCs have been constructed from cyclic block designs (see, e.g., [1,5,8,[10][11][12][13][14][15][16][17]22,23,25,29,30,43,47]). However, this also implies that it is a difficult task to determining the parameters for which an optimal 1-D OOC exists.…”

Near generalized balanced tournament designs with block sizes 4 and 5

“…{ (11,2), (7,2), (10,0), (4,1), ( (1,5), (6,7), (10,9), (15,9) (4,3), (3,5), (8,6),(15,7)} (3,0) { (5,3), (4,4), (10,6), (3,8), (1,8) 14), (2,14), (3,4), (4,9), { (1,13), (2,13), (3,2), (6,10), (8,4)} (2,0) (15,13) S1 : { (1,5), (2,10), (3,11), (4,9), …”