A method of constructing generalized difference sets

Research paper by B. T. Rumov

Indexed on: 01 Apr '74Published on: 01 Apr '74Published in: Mathematical Notes

Abstract

On the elements of the ring of residues modulo v (zτ v, 3τ v) we construct cyclic PBIB-designs with τ(v)-1 classes of connectedness, where τ(v) is the number of divisors of v. We prove the existence of cyclic BIB-designs with parameters b, v, r, k, and λ such that: 1) λ=k (and also λ=k/2 if k is even), k≥4, and (k-1) ¦ (p-1) for each prime divisor p of the number v; 2) λ=(k−l)/2, k odd, k≥3, k ¦ (p−1) for each prime divisor p of the number v.