摘要
Let (v,u × c,λ)-splitting BIBD denote a (v,u × c,λ)-splitting balanced incomplete block design of order v with block size u × c and index λ. The necessary conditions for the existence of a (v,u × c,λ)-splitting BIBD are v uc, λ(v-1) ≡ 0 0 mod (c(u-1)) and λv(v-1) ≡ 0 mod (c2u(u-1)). In this paper, for 2 λ 9 the necessary conditions for the existence of a (v,3 × 3,λ)-splitting BIBD are also suffcient with one possible exception for (v,λ) = (39,9).
Let (v, u × c,λ)-splitting BIBD denote a (v, u × c,λ)-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a (v, u × c,λ)-splitting BIBD are v ≥ uc, λ(v- 1) -- 0 0 mod (c(u- 1)) and Av(v- 1) - 0 mod (c^2u(u- 1)). In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a (v, 3 × 3, λ)-splitting BIBD are also sufficient with one possible exception for (v, λ) = (39, 9).
基金
the National Natural Science Foundation of China (No. 10771193)
the Starter Foundation for the Doctors of Zhejiang Gongshang University(No. 1020XJ030517)
the Natural Science Foundationof Universities of Jiangsu Province (No. 07KJB110090)
the Starter Foundation for the Doctors of Nantong University (No. 07B12)
关键词
代数
组合设计
信道编码
数学
Splitting
balanced incomplete block design
group-divisible design (GDD)