Design theory
Concerning difference families with block size four
Discrete Mathematics
Constructions of (q,k,1) difference families with q a prime power and k=4,5
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A survey on relative difference sets
GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster
Finite fields
From a (G, k, 1) to a (Ck ⊕ G, k, 1) Difference Family
Designs, Codes and Cryptography
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Discrete Mathematics
Existence of (q,6,1) Difference Families withq a Prime Power
Designs, Codes and Cryptography
On cyclically resolvable cyclic Steiner 2-designs
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Optimal (9v, 4, 1) Optical Orthogonal Codes
SIAM Journal on Discrete Mathematics
Constructions for optimal constant weight cyclically permutable codes and difference families
IEEE Transactions on Information Theory
Some progress on (v, 4, 1) difference families and optical orthogonal codes
Journal of Combinatorial Theory Series A
Cyclic Difference Packing and Covering Arrays
Designs, Codes and Cryptography
Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)
Designs, Codes and Cryptography
Covering arrays of strength 3 and 4 from holey difference matrices
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes
IEEE Transactions on Information Theory
New upper bound for (m, k, λ)-IRSs with λ ≥ 2
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
Combinatorial constructions for optimal two-dimensional optical orthogonal codes
IEEE Transactions on Information Theory
Two-dimensional optical orthogonal codes and semicyclic group divisible designs
IEEE Transactions on Information Theory
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
Problems of Information Transmission
Constructions of covering arrays of strength five
Designs, Codes and Cryptography
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Two classes of optimal two-dimensional OOCs
Designs, Codes and Cryptography
Semicyclic 4-GDDs and related two-dimensional optical orthogonal codes
Designs, Codes and Cryptography
Some 20-regular CDP(5,1;20u) and their applications
Finite Fields and Their Applications
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Finite Fields and Their Applications
| Hi-index | 0.24 |
We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4p—for any prime p \equiv 1 \pmod 6 such that (p−1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for p \equiv 1 \pmod 12. In this case an explicit construction was given for p \equiv 13 \pmod 24. Here, such an explicit construction is also realized for p \equiv 1 \pmod 24.We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime p \equiv 1 \pmod 6, p7. The existence is guaranteed for p(2q3−3q2+1)2+3q2 where q is the least prime factor of (p−1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6p for any prime p5 and the existence of a cyclic (4, 1)-GDD of type 8p for any prime p \equiv 1 \pmod 6. The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with λ=1.