We explore classical (relative) difference sets intersected with the cosets of a subgroup of small index. The intersection sizes are governed by quadratic Diophantine equations. Developing the intersections in the subgroup yields an interesting class of group divisible designs. From this and the Bose-Shrikhande-Parker construction, we obtain some new sets of mutually orthogonal latin squares. We also briefly consider optical orthogonal codes and difference triangle systems.
@article{10_37236_5641,
author = {Peter J. Dukes and Alan C.H. Ling},
title = {Relative difference sets partitioned by cosets},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/5641},
zbl = {1372.05024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5641/}
}
TY - JOUR
AU - Peter J. Dukes
AU - Alan C.H. Ling
TI - Relative difference sets partitioned by cosets
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/5641/
DO - 10.37236/5641
ID - 10_37236_5641
ER -
%0 Journal Article
%A Peter J. Dukes
%A Alan C.H. Ling
%T Relative difference sets partitioned by cosets
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5641/
%R 10.37236/5641
%F 10_37236_5641
Peter J. Dukes; Alan C.H. Ling. Relative difference sets partitioned by cosets. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/5641
