Design theory
Constructions of (q,k,1) difference families with q a prime power and k=4,5
Selected papers of the 14th British conference on Combinatorial conference
From a (G, k, 1) to a (Ck ⊕ G, k, 1) Difference Family
Designs, Codes and Cryptography
On Resolvable Difference Families
Designs, Codes and Cryptography
Some combinational constructions for optical orthogonal codes
Discrete Mathematics
Optimal (9v, 4, 1) Optical Orthogonal Codes
SIAM Journal on Discrete Mathematics
Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes
Designs, Codes and Cryptography
Construction for optimal optical orthogonal codes
Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
Combinatorial constructions of optimal optical orthogonal codes with weight 4
IEEE Transactions on Information Theory
Constructions for optimal constant weight cyclically permutable codes and difference families
IEEE Transactions on Information Theory
Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes
IEEE Transactions on Information Theory
Optimal variable-weight optical orthogonal codes via cyclic difference families
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On constructions for optimal two-dimensional optical orthogonal codes
Designs, Codes and Cryptography
Signature code designing for OCDMA system based on Steiner system on affine plane
AsiaCSN '08 Proceedings of the Fifth IASTED International Conference on Communication Systems and Networks
Combinatorial constructions for optimal two-dimensional optical orthogonal codes
IEEE Transactions on Information Theory
Further progress on difference families with block size 4 or 5
Designs, Codes and Cryptography
New optimal variable-weight optical orthogonal codes
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
New results on optimal (v, 4, 2, 1) optical orthogonal codes
Designs, Codes and Cryptography
SIAM Journal on Discrete Mathematics
Problems of Information Transmission
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Two classes of optimal two-dimensional OOCs
Designs, Codes and Cryptography
Some 20-regular CDP(5,1;20u) and their applications
Finite Fields and Their Applications
On cyclic 2(k -1)-support (n,k)k-1 difference families
Finite Fields and Their Applications
Combinatorial designs and the theorem of Weil on multiplicative character sums
Finite Fields and Their Applications
Combinatorial constructions for optimal 2-D optical orthogonal codes with AM-OPPTS property
Designs, Codes and Cryptography
| Hi-index | 0.12 |
Some new classes of optimal (v, 4, 1) optical orthogonal codes are constructed. First, mainly by using perfect difference families, we establish that such an optimal OOC exists for v ≤ 408, v ≠ 25. We then look at larger (p, 4, 1) OOCs with p prime; some of these codes have the nice property that the missing differences are the (r - 1)th roots of unity in Zp, (r being the remainder of the Euclidean division of p by 12) and we prove that for r = 5 or 7 they give rise to (rp, 4,1) difference families. In this way we are able to give a strong indication about the existence of (5p,4,1) and (7p,4, 1) difference families with p a prime ≡ 5, 7 mod 12 respectively. In particular, we prove that for a given prime p ≡ 7 mod 12, the existence of a (7p,4, 1) difference family is assured (1) if p Zp and we have 3 ≡ ωi (mod p) with gcd(i, p-1/6) v ≤ 601 for which a cyclic (v, 4, 1) difference family exists, and we give a few cyclic pairwise balanced designs with minimum block size 4.