Two Steiner triple systems, S 1 VY B 1 and S 2 VY B 2 , are orthogonal (S 1 c S 2 ) if B 1 B 2 Y and if fuY vg T fxY yg, uvwY xyw P B 1 , uvsY xyt P B 2 then s T t. The solution to the existence problem for orthogonal Steiner triple systems, (OSTS) was a major accomplishment in design theory. Two or
Cyclical Steiner triple systems orthogonal to their opposites
โ Scribed by Shmuel Schreiber
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 210 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
The binary linear codes generated by incidence matrices of the 80 Steiner triple systems on 15 points (STS( )) are studied. The 80 codes of length 35 spanned by incidence vectors of the points are all non-isomorphic. In contrast, a pair of codes of length 15 generated by blocks are isomorphic if and
## Phelps 2.1 will produce such a collection for each n -1/> 1. Choose U as in (3.1) above, then B,, =pBn-1 U U is a set of representatives for a CSTS(p"). Since every multiplier m =-1 (modp n'l) is an automorphism of this system f(x)=p"-lx2 +x will be an isomorphism from B,, to another CSTS(p~),