Construction of (v,k,1) cyclic difference families with small parameters

Baicheva Tsonka; Svetlana Topalova; Ivan Hetman

doi:10.13069/jacodesmath.v13i1.389

Baicheva Tsonka Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Svetlana Topalova 1) Institute of Mathematics and Informatics, Bulgarian Academy of Sciences; 2) Centre of Excellence in Informatics and Information and Communication Technologies
Ivan Hetman Lviv, Ukraine

DOI: https://doi.org/10.13069/jacodesmath.v13i1.389

Keywords: Cyclic difference families, Multipliers, Cyclic Steiner systems, Cyclically permutable constant weight codes, Optical orthogonal codes

Abstract

We construct all nonequivalent (v,k,1) cyclic difference families for 18 sets of parameters v and k for which classification results were not known. We also present the multipliers of all previously classified CDFs with small parameters. Most of the results are double-checked by two different backtrack search algorithms. The usage of an interesting property of the considered objects makes one of these algorithms faster than the other.