There exist nonisomorphic STS(19) with equivalent point codes

Reference:

Petteri Kaski and Patric R. J. Östergård. There exist nonisomorphic STS(19) with equivalent point codes. Journal of Combinatorial Designs, 12(6):443–448, 2004.

Abstract:

The rows of a point by block incidence matrix of a design can be used to generate a code, the point code of the design. It is known that binary point codes of nonisomorphic Steiner triple systems of order , STS(), are inequivalent when , but whether this also holds for higher orders has been open. In the current paper an example of two nonisomorphic STS(19) with equivalent point codes is presented.

Keywords:

code equivalence, design isomorphism, point code, Steiner triple system

Suggested BibTeX entry:

@article{KaOs04d,
    author = {Petteri Kaski and Patric R. J. {\"O}sterg{\aa}rd},
    journal = {Journal of Combinatorial Designs},
    number = {6},
    pages = {443--448},
    title = {There exist nonisomorphic {S}{T}{S}(19) with equivalent point codes},
    volume = {12},
    year = {2004},
}