Some cyclic BIBDs with block size four

Abstract

In this paper we give some results on cyclic BIBDs with block size 4. It is proved that a cyclic Bð4; 1; 4 n uÞ exists where u is a product of primes congruent to 1 modulo 6 and n is a positive integer and n ! 3. In the case of n ¼ 2, we also give some partial results on the existence of a cyclic Bð4; 1; 4 2 uÞ where u is a product of primes congruent to 1 modulo 6.

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.…”

Construction of weak universal optimal block designs with various correlation structures and block sizes

“…Some other foundational results about the construction of BIBD's with block size k = 3 or 4 are presented by Cheny and Wei (2006), Lam and Miao (1999), Cheng (1983) and Chang (2004). An example of BIBD: if we take k = 4, v = 5, then by formula (1) and (2), we can take r = 4, b = 5 and λ = 3.…”

The existence of cyclic (v,4,1)-designs

“…On the whole, it appears that no infinite family of cyclic (v, 4, 1)-design was known such that v can run over a congruent class and v is not a prime. For more information on cyclic (v, 4, 1)-designs, the reader is referred to [1,2,9,10].…”