Necessary conditions are obtained for the existence of a 2 - (v, k, λ) design, for which the block intersection sizes s1, s2, ..., sn satisfy s1 ≡s2 ≡ ... ≡sn ≡s (mod 2e), where e is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Applied Mathematics