On the existence of cyclic Steiner Quadruple Systems SQS(2p)
Discrete Mathematics - Special volume: Designs and Graphs
The last packing number of quadruples, and cyclic SQS
Designs, Codes and Cryptography
Optimal (9v, 4, 1) Optical Orthogonal Codes
SIAM Journal on Discrete Mathematics
The Steiner quadruple systems of order 16
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Note: Simple abelian quadruple systems
Journal of Combinatorial Theory Series A
Constructions for strictly cyclic 3-designs and applications to optimal OOCs with λ=2
Journal of Combinatorial Theory Series A
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Optical orthogonal codes: their bounds and new optimal constructions
IEEE Transactions on Information Theory
Combinatorial constructions of optimal optical orthogonal codes with weight 4
IEEE Transactions on Information Theory
A new recursive construction for optical orthogonal codes
IEEE Transactions on Information Theory
New constructions of optimal cyclically permutable constant weight codes
IEEE Transactions on Information Theory
Optical orthogonal codes obtained from conics on finite projective planes
Finite Fields and Their Applications
IEEE Journal on Selected Areas in Communications
Hi-index | 754.84 |
An optical orthogonal signature pattern code (OOSPC) finds application in transmitting 2-D images through multicore fiber in code-division multiple-access (CDMA) communication systems. Observing a one-to-one correspondence between an OOSPC and a certain combinatorial subject, called a packing design, we present a construction of optimal OOSPCs with weight 4 and maximum collision parameter 2, which generalizes a well-known Köhler construction of optimal optical orthogonal codes (OOC) with weight 4 and maximum collision parameter 2. Using this new construction enables one to obtain infinitely many optimal OOSPCs, whose existence was previously unknown. We prove that for a multiple n of 4, there exists no optimal OOSPC of size 6 × n with weight 4 and maximum collision parameter 2, together with a report which shows a gap between optimal OOCs and optimal OOSPCs when 6 and n are not coprime. We also present a recursive construction of OOSPCs which are asymptotically optimal with respect to the Johnson bound. As a by-product, we obtain an asymptotically optimal (m, n, 4, 2)-OOSPC for all positive integers m and n.